Electric machine

ABSTRACT

An electric machine comprise a first carrier having an array of electromagnetic elements and a second carrier having electromagnetic elements defining magnetic poles, the second carrier being arranged to move relative to the first carrier. An airgap is provided between the first carrier and the second carrier. The electromagnetic elements of the first carrier include posts, with slots between the posts, one or more electric conductors in each slot, the posts of the first carrier having a post height in mm. The first carrier and the second carrier together define a size of the electric machine. The magnetic poles having a pole pitch in mm. The size of the motor, pole pitch and post height are selected to fall within a region in a space defined by size, pole pitch and post height that provides a benefit in terms of force or torque per weight per excitation level.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a non-provisional application that claims priorityto U.S. Provisional Patent Application No. 62/203,903, entitled “HighPower Density Electromagnetic Machine,” filed Aug. 11, 2015; U.S.Provisional Patent Application No. 62/209,333, entitled “High PowerDensity Electromagnetic Machine,” filed Aug. 24, 2015; U.S. ProvisionalPatent Application No. 62/292,860, entitled “High Power DensityElectromagnetic Machine,” filed Feb. 8, 2016; U.S. Provisional PatentApplication No. 62/322,217, entitled “Electric Machine,” filed Apr. 13,2016; and U.S. Provisional Patent Application No. 62/363,202, entitled“Electric Machine,” filed Jul. 15, 2016. Each of the applications listedabove is incorporated by reference herein in its entirety.

TECHNICAL FIELD

Electric machines.

BACKGROUND

In the design of electric machines, it is known to select structuralparameters such as slot number depending on the intended application anddesired performance characteristics of the machine. However, not allvalues of the structural parameters are used in practice. There is roomfor improved performance of electric machines, particularly in robotics.

Electric machines typically use electrically conductive wire turnswrapped around soft magnetic stator posts (teeth) to generate flux. Themanufacturing process for this type of motor construction can be timeconsuming and expensive. As well, such motors typically have a torque tomass ratio that makes them relatively heavy for mobile actuatorapplications such as in robotics where the weight of a downstreamactuator must be supported and accelerated by an upstream actuator.

SUMMARY

The inventor has proposed an electric machine with a novel range ofstructural parameters particularly suited for robotics, along withadditional novel features of an electric machine. The features forexample relate to improved heat dissipation resulting from the structureof electromagnetic elements as well as features that relate to rigidityof the electric machine, conductor design, cooling, rotor design, statordesign and operating parameters.

In an embodiment, an electric machine comprises a first carrier havingan array of electromagnetic elements and a second carrier havingelectromagnetic elements defining magnetic poles, the second carrierbeing arranged to move relative to the first carrier. An airgap isprovided between the first carrier and the second carrier. Theelectromagnetic elements of the first carrier include posts, with slotsbetween the posts, one or more electric conductors in each slot, theposts of the first carrier having a post height in mm. The first carrierand the second carrier together define a size of the electric machine.The magnetic poles having a pole pitch in mm. The size of the motor,pole pitch and post height are selected to fall within a region in aspace defined by size, pole pitch and post height that provides abenefit in terms of force or torque per weight per excitation level. Theelectromagnetic elements defining magnetic poles may be permanentmagnets.

There is provided an electric motor comprising a stator comprisingelectromagnetic elements, the stator having posts on one side and abackiron having cooling fins on an opposite side, the stator comprisinga unitary piece of material including at least portions of the posts andat least portions of the cooling fins. In various embodiments, there maybe included any one or more of the following features: The posts mayhave a post width in the circumferential direction, and the backironincluding the fins may have a height greater than 50% of the post width.The fins may have tips comprising a different material than the unitarypiece of material. The electric motor may be an axial flux motor. Thecooling fins may be spiral shaped. The electric motor may have a rotorhaving electromagnetic elements defining magnetic poles, the rotor beingarranged to rotate relative to the stator, the magnetic poles having apole pitch S in mm, an airgap between the stator and the rotor, posts ofthe stator having a post height in mm, the stator and the rotor togetherdefining a size of the electric machine, the size of the motor, polepitch and post height being selected to fall within a region in a spacedefined by size, pole pitch and post height that provides a benefit interms of force or torque per weight per excitation level.

There is also provided an electric motor comprising a rotor arranged forrotation relative to one or more stators comprising electromagneticelements, the rotor comprising a permanent magnet carrier loaded withpermanent magnets, an output ring, and bearings for supporting the rotorfor rotation, the bearings located intermediate between the permanentmagnet carrier and the output ring. In various embodiments, there may beincluded any one or more of the following features: the motor may be anaxial flux motor, and the one or more stators may be two stators and therotor may be arranged between the two stators. The bearings may bepreloaded by magnetic forces between the rotor and stators. The rotormay have two axial sides, and comprises magnets on each axial side ofthe rotor, the magnets on each axial side oriented tangentially, andeach magnet aligned axially with a respective magnet on the other axialside, the tangential orientation of each magnet being opposite to thetangential orientation of the respective magnet on the other side. Theone or more stators may comprise spiral cooling fins.

There is also provided an electric motor comprising a rotor arranged onbearings for rotation between two stators from which the rotor isseparated by airgaps, a magnetic force between the rotor and statorsattracting the stators to the rotor and applying a preloading force onthe bearings. In various embodiments, there may be included any one ormore of the following features: the rotor may have an output ringlocated radially inward from the magnets.

The bearings may have outer diameter (OD) races attached to the rotor.The rotor may have an output ring located radially outward from themagnets. The bearings may have inner diameter (ID) races attached to therotor. The airgaps may close by more than 50% as a result of magneticforce if the bearings are not present in the assembly. The stators androtor may come into contact if the bearings are not present in theassembly. There may be axial inward facing surfaces of a housing and thebearings may have axial outward facing bearing races contacting theaxial inward facing surfaces of the housing, and the axial inward facingsurfaces of the housing may deform under magnetic load such that thedifference in position between the position of the axial inward facingsurfaces and a hypothetical position of the inward facing surface if nobearings are present is greater than 0.002″.

These and other aspects of the device and method are set out in theclaims.

BRIEF DESCRIPTION OF THE FIGURES

Embodiments will now be described with reference to the figures, inwhich like reference characters denote like elements, by way of example,and in which:

FIG. 1 is a CAD model of a complete exemplary actuator prototype.

FIG. 2 is a section view of the exemplary actuator in FIG. 1.

FIG. 3 shows a side view detail of the stator and rotor of the exemplaryactuator in FIG. 1.

FIG. 4 shows a schematic of the entire stator and rotor of the exemplaryactuator in FIG. 1.

FIG. 5 shows a simplified schematic section view of the stator and rotorof the exemplary actuator in FIG. 1, with schematic CAD model coils onthe posts.

FIG. 6 shows a non-limiting simplified exemplary embodiment of a statorof a linear electric machine.

FIG. 7 shows an isometric view of the stator in FIG. 6.

FIG. 8 shows a top view of the stator in FIG. 6 and FIG. 7 with theupper insulator layer removed.

FIG. 9 shows top view of the stator in FIG. 8 with the two upper phasecircuits removed.

FIG. 10 is a sectional view of the stator of FIG. 6 to FIG. 9.

FIG. 11 is a detail view of the cross section shown in FIG. 10.

FIG. 12 shows an isometric view of a non-limiting exemplary linearelectric machine.

FIG. 13 shows the electric machine of FIG. 12 with internal lines.

FIG. 14 shows the electric machine of FIG. 12 with the upper permanentmagnet carrier backiron removed.

FIG. 15 shows the electric machine of FIG. 14 with upper permanentmagnet carrier plate and most of the upper permanent magnets removed.

FIG. 16 shows the electric machine of FIG. 15 with all permanent magnetsremoved and the top insulator plate removed.

FIG. 17 shows the electric machine of FIG. 16 with the electricalconnectors removed and the top spacer layer removed.

FIG. 18 shows the electric machine of FIG. 17 with the top phase circuitconductor removed and the second insulator layer removed.

FIG. 19 shows the electric machine of FIG. 18 with the second spacerlayer removed and most of the posts removed.

FIG. 20 shows the electric machine of FIG. 19 with the upper air coresensor, the second phase circuit, the structural cylindrical spacers,and the rest of the posts removed.

FIG. 21 shows the electric machine of FIG. 20 with the third phasecircuit and the bottom spacer layer removed.

FIG. 22 shows the conductor circuits, posts, and potting compound ringfor a non-limiting exemplary embodiment of an axial flux, rotary statorelectric machine.

FIG. 23 shows a detail view of the stator in FIG. 22.

FIG. 24 an axial flux, rotary stator with three phases and one conductorcircuit per phase, with the potting compound ring removed.

FIG. 25 is an isometric view of three phase circuits with soft magneticmaterial posts positioned by the aluminum circuits during assembly.

FIG. 26 is an exploded view of FIG. 25.

FIG. 27 is a closeup of an individual layer of the embodiment of FIG. 25and FIG. 26.

FIG. 28 is a closeup of an individual layer of the embodiment of FIG. 25and FIG. 26.

FIG. 29 is a top view detail of a single stator circuit.

FIG. 30 shows sections of an axial flux electric machine.

FIG. 31 shows an array of electromagnetic elements (here, coils) in alinear electric machine facing electromagnetic elements (here, permanentmagnets) across an airgap.

FIG. 32 illustrates a sectioned axial flux electric machine with a loadarm.

FIG. 33 shows a stator of an axial flux electric machine;

FIG. 34 is a detail of the stator of FIG. 33.

FIG. 35 is detail of electric conductor layers for use in the stator ofFIG. 33.

FIG. 36 is further detail of electric conductor layers for use in thestator of FIG. 33.

FIG. 37 is further detail of an electric conductor layer for use in thestator of FIG. 33.

FIG. 38 shows electric conductor layers of the stator of FIG. 33.

FIG. 39 shows electric conductor layers of the stator of FIG. 33.

FIG. 40 shows an embodiment of robotic arms that may be equipped at thejoints with an embodiment of the disclosed electric machine.

FIG. 41 shows an embodiment of robotic arms that may be equipped at thejoints with an embodiment of the disclosed electric machine.

FIG. 42 shows a magnet configuration for an embodiment of the disclosedelectric machine.

FIG. 43 is a first figure of detail showing successive layers of alinear electric machine.

FIG. 44 is a second figure of detail showing successive layers of alinear electric machine.

FIG. 45 is a third figure of detail showing successive layers of alinear electric machine.

FIG. 46 is a fourth figure of detail showing successive layers of alinear electric machine.

FIG. 47 shows details of connections for connecting layers of a linearelectric machine to a multiphase source of electric excitation

FIG. 48 shows details of connections for connecting layers of a linearelectric machine to a multiphase source of electric excitation

FIG. 49 is a first figure showing successive layers of an embodiment ofa liner electric machine.

FIG. 50 is a second figure showing successive layers of an embodiment ofa liner electric machine.

FIG. 51 is a third figure showing successive layers of an embodiment ofa liner electric machine.

FIG. 52 is a fourth figure showing successive layers of an embodiment ofa liner electric machine.

FIG. 53 shows an embodiment of an electric machine with coils in bothrotor and stator.

FIG. 54 shows an embodiment of an electric machine with coils in bothrotor and stator.

FIG. 55 shows an embodiment of an electric machine with a Hallbach arrayof magnets.

FIG. 56 shows a cross-section of an exemplary actuator assembly with atwo-part stator, three phases and a 3:2 stator post:permanent magnetratio.

FIG. 57 shows a detailed cross-section view of the embodiment from FIG.56.

FIG. 58 shows the torque plotted as a function of rotor position for a3:2 ratio or stator posts:permanent magnets, demonstrating the effect ofrotating one stator relative to the other.

FIG. 59 shows an exploded view of the exemplary embodiment in FIG. 56.

FIG. 60 shows a cross section of a partially exploded view of theexemplary embodiment in FIG. 56.

FIG. 61 show a section detail view of a housing of the exemplaryembodiment in FIG. 56.

FIG. 62 shows a section of an assembled housing and stator of theexemplary embodiment in FIG. 56.

FIG. 63 shows a section of an assembled housing and stator of theexemplary embodiment in FIG. 56 with the first conductor layer on thestator.

FIG. 64 shows a plan view of the section in FIG. 63.

FIG. 65 shows four conductor layers of the same phase from the exemplaryembodiment in FIG. 56.

FIG. 66 shows the arrangement of three adjacent conductor layers fromdifferent phases from the exemplary embodiment in FIG. 56.

FIG. 67 shows a section of an assembled housing and stator from theexemplary embodiment in FIG. 56 with radial fluid flow channels betweenconductors indicated.

FIG. 68 shows a plan view of the radial, axial and circumferential fluidflow paths for cooling fluid between the conductors of the exemplaryembodiment in FIG. 56.

FIG. 69 shows a section view through the stator of FIG. 68 showing thecooling fluid flow path.

FIG. 70 shows a cross-sectional view of an exemplary embodiment with twostators and a rotor.

FIG. 71 shows a stator from the exemplary embodiment in FIG. 70 withconductors shown in one section.

FIG. 72 shows a section view of a simplified stator with conductors.

FIG. 73 shows an exemplary configuration of conductors on a stator inwhich the conductors do not skip slots.

FIG. 74 shows an exemplary configuration of conductors on a stator inwhich some conductors with variable conductor widths.

FIG. 75 shows an exploded view of four layers of conductors from FIG.74.

FIG. 76 shows an exemplary configuration of conductors with multi-layerthickness fluid flow gaps.

FIG. 77 shows a configuration of conductor layers in an exemplary methodof assembly.

FIG. 78 shows an exemplary configuration of conductors without radialfluid flow gaps.

FIG. 79 shows an exemplary embodiment of a stator with curved,variable-width posts.

FIG. 80 shows an exemplary embodiment of a rotor with tangentiallyoriented permanent magnets and radially extending flux path members.

FIG. 81 shows a detail view of the rotor in FIG. 80.

FIG. 82 shows the structural connection between the inward members andinner part of the rotor in FIG. 80.

FIG. 83 shows the structural connection between the outward members andouter part of the rotor in FIG. 80.

FIG. 84 shows a detail view of the rotor in FIG. 80 with the magnetsremoved.

FIG. 85 shows an expanded view of the rotor in FIG. 80 reflecting anexemplary method of assembly.

FIG. 86 shows a view of the rotor in FIG. 60 with the inner rotor ringand outwardly projecting flux members shown in black.

FIG. 87 shows an exemplary embodiment of a rotor comprising two axialhalves and tapered magnets.

FIG. 88 shows a section view of the rotor in FIG. 87.

FIG. 89 shows an exploded view of the rotor in FIG. 87.

FIG. 90 shows the plane view of the magnets in the rotor in FIG. 87,showing the polarity of the magnets.

FIG. 91 shows the structural connection between the outward members andouter part of the rotor in FIG. 87.

FIG. 92 shows the rotor in FIG. 87 with an external ring holding therotor halves together.

FIG. 93 shows an exploded view of an exemplary embodiment comprising tworotor halves and two stator halves.

FIG. 94 shows a cross-section view of the embodiment in FIG. 93.

FIG. 95 shows a stator in the embodiment shown in FIG. 93.

FIG. 96 shows an exploded view of the stators and baseplate of theembodiment in FIG. 93.

FIG. 97 shows a section view of the embodiment in FIG. 93.

FIG. 98 shows a cross-section view of an exemplary embodiment with tworotor halves and one stator.

FIG. 99 shows a section view of the exemplary embodiment in FIG. 98.

FIG. 100 shows an exemplary configuration of a robotic arm having aseries of electric machines acting as actuators and being spaced alongthe arm.

FIG. 101 shows a mounting configuration for an electric machine on arobotic arm.

FIG. 102 shows an embodiment of a rotor configuration.

FIG. 103 shows an exemplary configuration of a laminated post stator.

FIG. 104 shows a section view of an exemplary embodiment of a statorwith radially aligned post laminations.

FIG. 105 shows an exemplary embodiment of a laminated post constructionwith posts extending through the backiron, with tapered barbs asmechanical pull-out stops.

FIG. 106 is a section view of the embodiment shown in FIG. 105.

FIG. 107 is a section view of the embodiment shown in FIG. 105, showingthe pattern of insulation between laminations and a portion of theresulting magnetic flux path.

FIG. 108 is a schematic drawing showing the effect of anodizing a sharpedge.

FIG. 109 is a schematic drawing of a stator section comprisingconductors with rounded edges.

FIG. 110 is a schematic drawing of a stator section comprisingconductors with sharp edges.

FIG. 111 is a perspective view of two adjacent layers of stackable flatconductors shown side by side before assembly.

FIG. 112 is a schematic drawing showing an example of a coatedconductor, with dielectric coating over the surface of an anodizedconductor

FIG. 113 is a closeup of a corner of the conductor of FIG. 112.

FIG. 114 is a perspective view showing conductors stacked together intolayers with the conductor pair stacked between stator posts.

FIG. 115 is a schematic drawing showing an example of a coatedconductor, with complete coverage of the gaps at the sharp edges.

FIG. 116 is a schematic drawing showing an example of a coatedconductor, with more than complete coverage of the gaps at the sharpedges.

FIG. 117 is a schematic drawing showing an example of a coated conductorof FIG. 115, coated with a further polymer layer.

FIG. 118 shows a section view of an assembled stator and conductors witha spacer between one or more conductor layers in one or more slots

FIG. 119 shows a section view of the conductors and spacers beforespacer removal with the powder edge coating contacting and adhering theconductors to each and/or to the post sidewalls.

FIG. 120 shows a simplified section of stator with a spacer componentbeing removed.

FIG. 121 shows a method of making anodized conductors;

FIG. 122 shows a further detail of a method of making anodizedconductors;

FIG. 123 shows a cross-section of an embodiment of a conical rotor;

FIG. 124 shows a close-up cross-sectional view of the embodiment in FIG.123;

FIG. 125 shows a close-up cross-sectional view of the embodiment in FIG.123;

FIG. 126 shows a close-up cross-sectional view of the embodiment in FIG.123;

FIG. 127 shows a close-up cross-sectional view of the embodiment in FIG.123;

FIG. 128 is an axial view of an embodiment of an assembled actuatorincluding power and encoder connectors.

FIG. 129 is a section view of the actuator of FIG. 128 showing aninternal rotor along a centre plane between two stators.

FIG. 130 is an isometric section view of a stator and housing assemblyof the actuator of FIG. 128 with a partial section of layeredconductors.

FIG. 131 is an axial view of a stator, inner housing, outer housing, andlayered conductors of the actuator or FIG. 128.

FIG. 132 is an isometric view of rotor components of the embodiment ofFIG. 128.

FIG. 133 is a side view of a rotor and stators with an example magnetarrangement in which adjacent magnets are oppositely tangentiallypolarized.

FIG. 134 is a perspective view of an actuator including a separationmember to separate two stators.

FIG. 135 is another section view of the stator for the actuator of FIG.128, showing a magnetic flux path through cooling fins.

FIG. 136 is a section view of a stator with cooling fins showing a crosssectional area for flux linkage at a diagonal between posts.

FIG. 137 is a simplified section view of a stator with circumferentialcooling fins.

FIG. 138 is a section view of an actuator including a separation memberconfigured to reduce preload on inner bearings.

FIG. 139 is a section view of an actuator including a separation memberconfigured to enhance preload on inner bearings.

FIG. 140 is a cross sectional view of an actuator having sealed coolingchannels.

FIG. 140A is a perspective view of an embodiment having semi-circularcooling channels.

FIG. 140B is a cross-section view of an embodiment with two stators anda rotor, with a housing connected by an inner diameter rigid connection.

FIG. 140C is an expanded cross-section view of the embodiment shown inFIG. 140B.

FIG. 141 is a simplified section view of a linear embodiment of aconcentrated flux rotor.

FIG. 142 is a model of a concentrated flux rotor with back iron showingmagnetic flux lines.

FIG. 143 is a model of a concentrated flux rotor with back iron showingmagnetic flux lines, further showing component lengths.

FIG. 144 is a cross-section through a segment of an axial fluxconcentrated flux rotor with tapered magnets and flux path restrictions.

FIG. 145 is a close-up section view of a portion of an axial fluxconcentrated flux rotor with extended length magnets.

FIG. 146 is a simplified angled cross-section of an embodiment of aradial flux concentrated flux rotor with stator.

FIG. 147 is a simplified section view of the radial flux concentratedflux rotor and stator shown in FIG. 146.

FIG. 148 is a simplified angled cross-section of the concentrated fluxrotor shown in FIG. 146, further showing mills.

FIG. 149 is a model of a concentrated flux rotor with back iron withvariant geometries and showing magnetic flux lines.

FIG. 150 is a simplified angled cross-section of an embodiment of aradial flux concentrated flux rotor with rotor reliefs and tapered rotorends.

FIG. 151 is a simplified exploded section view of an embodiment of anaxial flux stator-rotor-stator configuration of a concentrated fluxrotor with end iron.

FIG. 152 is a simplified exploded section view of an embodiment of anaxial flux stator-rotor-stator configuration of a concentrated fluxrotor with back iron, end iron and flux path restrictions.

FIG. 153 is a simplified exploded section view of an embodiment of anaxial flux rotor-stator-rotor configuration of a concentrated flux rotorwith end irons and flux path restrictions.

FIG. 154 is a simplified exploded section view of an embodiment of anaxial flux rotor-stator-rotor configuration of a concentrated flux rotorwith end irons, flux path restrictions and back irons.

FIG. 155 is a simplified exploded section view of an embodiment of atrapezoidal stator-rotor-stator configuration of a concentrated fluxrotor with back irons and end irons

FIG. 156 is simplified exploded section view of the embodiment shown inFIG. 155 without back irons.

FIG. 157 is a simplified exploded section view of an embodiment of atrapezoidal rotor-stator-rotor configuration of a concentrated fluxrotor with end irons.

FIG. 158 is a simplified exploded section view of the embodiment shownin FIG. 157 with back irons and without end irons.

FIG. 159 is a simplified perspective view of an embodiment of arotor-stator-rotor configuration linear flux machine with back irons andend irons.

FIG. 160 is a simplified perspective view of the embodiment shown inFIG. 159 without back irons.

FIG. 161 is a simplified perspective view of an embodiment of astator-rotor-stator configuration of a linear flux machine with backiron.

FIG. 162 is a simplified perspective view of an embodiment of astator-rotor-stator configuration of a linear flux machine with endirons, showing an angled cross-section of the rotor.

FIG. 163 is a model of an axial motor concentrated flux rotor withinterrupted rotor posts.

FIG. 164 is the model of an axial motor concentrated flux rotor shown inFIG. 164 with magnetic flux lines shown.

FIG. 165 is a cross-section of an embodiment of a transverse fluxmachine in which flux links across the air gap in the radial direction.

FIG. 166A is a perspective view of the stator of the embodiment of atransverse flux machine shown in FIG. 165.

FIG. 166B is a perspective view of an upper portion of the rotor of theembodiment of a transverse flux machine shown in FIG. 165.

FIG. 167 is a cross-section of an embodiment of a transverse fluxmachine in which flux links across air gaps in the axial direction.

FIG. 168 is a perspective view of a stator section of the embodiment ofa transverse flux machine shown in FIG. 167

FIG. 169 is a cross-section of an upper portion of the rotor of theembodiment of a transverse flux machine shown in FIG. 168.

FIG. 170A shows a graph of torque at constant current density for asimulated series of motors differing in slot pitch and post height.

FIG. 170B shows the highest stator current density possible at a giventemperature for a simulated series of motors differing in slot pitch andpost height.

FIG. 170C shows constant temperature torque as a function of slot pitchand post height for a series of electric machines.

FIG. 170D shows the value of a weighting function for at the higheststator current density possible at a given temperature for a simulatedseries of motors differing in slot pitch and post height.

FIG. 170E shows K_(m)″ for a simulated series of motors differing inslot pitch and post height, for a fixed current density.

FIG. 170F shows K_(R)″ for a simulated series of motors differing inslot pitch and post height, for a fixed current density.

FIG. 171 shows the region of benefit for K_(R)″, with respect to therest of the geometries in the domain, for a machine with 200 mm size anda boundary line for K_(R)″>1.3

FIG. 172 shows the region of benefit for K_(R)″, with respect to therest of the geometries in the domain, for a machine with 200 mm size anda boundary line for K_(R)″>1.5

FIG. 173 shows the region of benefit for K_(R)″, with respect to therest of the geometries in the domain, for a machine with 200 mm size anda boundary line for K_(R)″>1.8

FIG. 174 shows the region of benefit for K_(R)″, with respect to therest of the geometries in the domain, for a machine with 100 mm size anda boundary line for K_(R)″>1.5

FIG. 175 shows the region of benefit for K_(R)″, with respect to therest of the geometries in the domain, for a machine with 100 mm size anda boundary line for K_(R)″>1.7

FIG. 176 shows the region of benefit for K_(R)″, with respect to therest of the geometries in the domain, for a machine with 100 mm size anda boundary line for K_(R)″>1.9

FIG. 177 shows the region of benefit for K_(R)″, with respect to therest of the geometries in the domain, for a machine with 50 mm size anda boundary line for K_(R)″>2.2

FIG. 178 shows the region of benefit for K_(R)″, with respect to therest of the geometries in the domain, for a machine with 50 mm size anda boundary line for K_(R)″>2.5

FIG. 179 shows the region of benefit for K_(R)″, with respect to therest of the geometries in the domain, for a machine with 50 mm size anda boundary line for K_(R)″>2.9

FIG. 180 shows the region of benefit for K_(R)″, with respect to therest of the geometries in the domain, for a machine with 25 mm size anda boundary line for K_(R)″>3.3

FIG. 181 shows the region of benefit for K_(R)″, with respect to therest of the geometries in the domain, for a machine with 25 mm size anda boundary line for K_(R)″>3.4

FIG. 182 shows the region of benefit for K_(R)″, with respect to therest of the geometries in the domain, for a machine with 25 mm size anda boundary line for K_(R)″>3.6

FIG. 183 is a graph showing the sum of the eddy current and hysteresislosses for a motor series across a range of slot pitches at a rotorspeed of 200 rpm with no current applied.

FIG. 184 is a graph showing torque for 24 slot laminated M-19 and solidM-19 stators with an applied current density of 6 A/mm2.

FIG. 185 is a graph showing individual and total stator losses for a 24slot solid M-19 stator;

FIG. 186 is a graph showing individual and total stator losses for a 108slot solid M-19 stator.

FIG. 187 is a graph showing torque for a 108-slot durabar, laminatedM-19 and solid M-19 stators with an applied current density of 19.7A/mm2.

FIG. 188 is a graph showing a torque-to-weight comparison for variousmotors in a simulation in which very strong NdFeB N52 permanent magnetswere used in the rotor.

FIG. 189 is a graph showing a torque comparison for various motors.

FIG. 190 is a graph showing a stator loss comparison for various motors.

FIG. 191 shows a method of cooling an actuator via a flow channel.

FIG. 192 is a section view of an embodiment of an actuator assembly.

FIG. 193A is a closeup section view of the actuator assembly of FIG.192.

FIG. 193B is a further closeup of bushings or low friction coating inthe section view of the actuator assembly of FIG. 193A.

FIG. 194 is a section view of a stator and fixed ring of the actuatorassembly of FIG. 192.

FIG. 195 is a closeup view of an embodiment of a stator for the actuatorassembly of FIG. 192, the arrows indicate how the conductors can beplace onto the posts over top of the extensions.

FIG. 196 is a closeup section view of the actuator assembly of FIG. 192with one stator and the corresponding bushings or low friction coatingremoved.

FIG. 197 is a section view of a permanent magnet carrier for theactuator assembly of FIG. 192.

FIG. 198 is a closeup section view of a rotor and stator of the actuatorassembly of FIG.

FIG. 199A is an axial isometric view of stator and rotor posts of theactuator assembly of FIG. 192.

FIG. 199B is a further closeup of stator and rotor posts of the actuatorassembly of FIG. 199A.

DETAILED DESCRIPTION

Immaterial modifications may be made to the embodiments described herewithout departing from what is covered by the claims. In the claims, theword “comprising” is used in its inclusive sense and does not excludeother elements being present. The indefinite articles “a” and “an”before a claim feature do not exclude more than one of the feature beingpresent. Each one of the individual features described here may be usedin one or more embodiments and is not, by virtue only of being describedhere, to be construed as essential to all embodiments as defined by theclaims.

DEFINITIONS

Several terms to be used throughout the text will first be defined.

A carrier, as used here in the context of electric machines, maycomprise a stator or a rotor when referring to rotary machines.

A rotor as used herein may be circular. A rotor may also refer thearmature or reaction rail of a linear motor. A stator may be circular.It may also refer to the armature or reaction rail of a linear motor.

Teeth may be referred to as posts.

In an electric motor, either a stator or rotor may have a commutatedelectromagnet array defined by coils wrapped around posts, while theother of the stator or rotor may have magnetic poles defined bypermanent magnets or coils or both coils and permanent magnets.

Permanent magnets may be used in combinations with electromagnets on therotor and/or stator to add flux to the system. PM means permanentmagnet. EM means electromagnet.

Electromagnetic elements may comprise permanent magnets, posts (teeth),slots defined by magnetic posts, which may be soft magnetic posts, andelectrical conductors. In any embodiment where one carrier has slots andposts, the other may have permanent magnets for the electromagneticelements, and for any such embodiment, the term electromagnetic elementmay be replaced by the term permanent magnet. Magnetic poles in somecases, for example in a concentrated flux rotor embodiment, may bedefined by permanent magnets in conjunction with adjacent posts in whicha magnetic field is established by the permanent magnets.

Unless otherwise specified, “flux” refers to magnetic flux.

A fractional slot motor is a motor with a fractional number of slots perpole per phase. If the number of slots is divided by the number ofmagnets, and divided again by the number of phases and the result is notan integer, then the motor is a fractional slot motor.

A carrier may be supported for motion relative to another carrier by aframe or bearings, and the bearings may be sliding, roller, fluid, airor magnetic bearings. An axial electric machine is an electric machinein which magnetic flux linkage occurs across an axial airgap, and thecarriers are in the form of discs mounted coaxially side by side. Afirst carrier can be arranged to move relative to another carrier byeither carrier being supported by a frame, housing or other element,while the other carrier moves relative the first carrier.

A radial electric machine is an electric machine where the airgap isoriented such magnetic flux is radially oriented, and the carriers aremounted concentrically, one outside the other. A linear actuator iscomparable in construction to a section of an axial flux or radial fluxrotary motor where the direction of motion is a straight line ratherthan a curved path.

A trapezoidal electric machine is an electric machine that is acombination of both an axial and radial flux machines, where the planeof the airgap lies at an angle partway between the planes formed by theairgaps in the axial and radial configurations.

The airgap diameter for a rotary machine is defined as the diameterperpendicular to the axis of rotation at the centre of the airgapsurface. In radial flux motors, all of the airgap resides at the samediameter. If the airgap surface is a disc-shaped slice as in axial fluxmotors, the average airgap diameter is the average of the inner andouter diameter. For other airgap surfaces such as a diagonal or curvedsurfaces, the average airgap diameter can be found as the average airgapdiameter of the cross-sectional airgap view.

For a radial flux motor, the airgap diameter refers to the average ofthe rotor inner diameter and stator outer diameter (for an outer rotorradial flux motor) or the average of the rotor airgap outer diameter andstator airgap inner diameter (for an inner rotor radial flux motor).Analogues of the airgap diameter of a radial flux motor may be used forother types of rotary motors. For an axial flux machine, the airgapdiameter is defined as the average of the PM inner diameter and PM outerdiameter and EM inner diameter and EM outer diameter.

Size of an electric machine means the airgap diameter of an axial fluxmachine or radial flux machine as defined herein or the length in thedirection of translation of the carriers of a linear machine. For linearmachines where one carrier is longer than another, then the length isthe length of the shorter carrier. For use with reference to theboundary inequalities, the size of a rotary machine is given in terms ofdiameter, but for a linear machine it is the length that corresponds toa circumference of a rotary machine. Therefore, the size X of a linearmotor that corresponds in the equations to a rotary motor of size Y isrelated to Y as X=pi*Y. This size of any rotary electric machine for thepurpose of the disclosed range, as a general principle and includingtransverse flux machines, is defined as the average of the largest andsmallest diameters defined by the magnetically active airgap when it isprojected onto the plane that is perpendicular to the axis of rotation

The back surface of the stator is defined as the surface on the oppositeside of the stator to the surface which is at the magnetically activeairgap. In a radial flux motor, this would correspond to either theinner surface of the stator for an outer rotor configuration, or theouter diameter surface of the stator for an inner rotor configuration.In an axial flux motor, the back surface of the stator is the axiallyouter surface of the stator.

K_(m) is defined as the stall torque divided by the square root of theelectrical resistive losses of a motor. In this patent document, it isproposed to assess motor performance using K_(m) divided by the activemagnetic mass of the motor, referred to in this disclosure as KR orK_(R). The active magnetic mass consists of the rotor and stator massincluding magnets, coils, teeth, and backiron as is commonly reported bythe manufacturers of frameless motors. The K_(R) metric may be useful inassessing motor performance for applications where a low motor mass isbeneficial to overall power consumption, such as robotics. In somecases, size-independent analogues of K_(m) and K_(R), namely K_(m)″ andK_(R)″ are used throughout the text. The conversion between thesize-dependent and size-independent metrics is:

$K_{m} = \frac{K_{m}^{''}\sqrt{\pi \; L}D^{3/2}}{2}$ and${K_{R} = \frac{K_{R}^{''}\sqrt{{D/\pi}\; L}}{2}},$

where D is the average airgap diameter and L is the radial tooth length.For a given size of motor, D and L are taken to be fixed in theanalysis, therefore K_(R) or K_(m) will be proportional to K_(R)″ orK_(m)″. Consequently, statements relating to trends in K_(R) will, ingeneral, implicitly be held to apply to K_(R)″ as well.

Slot density is the number of slots divided by the circumferentiallength of machine at the average airgap diameter. If the pitch of theslots varies, the average slot density of a device will be used. Slotdensity can also be represented by the inverse of the slot pitch. It isa measure of how many slots occur per mm of circumferential length alongthe airgap at the airgap diameter (or its analogue). For rotary motors,it has the following equation:

${{Slot}\mspace{14mu} {density}} = \frac{N_{s}}{\pi \; D_{AG}}$

where N_(S) is the number of slots, and D_(AG) is the diameter of theairgap. For the case of a linear motor, the denominator of this functionwould be replaced by the length of the carrier along the direction oftranslation.

Pole density is the number of poles divided by the circumferentiallength of machine at the average airgap diameter. If the pitch of thepoles varies, the average pole density of a device will be used. Poledensity can also be represented by the inverse of the pole pitch. Thepole pitch is defined as the average distance at the average airgapbetween the center of a PM pole of one polarity to the center of thenext PM pole on the same carrier having the opposite polarity, measuredalong the direction of motion. In rotary motors this distance is acircumferential pitch measured at the average airgap diameter, DAG. Itis a measure of how many poles occur per mm of circumferential lengthalong the airgap at the airgap diameter (or its analogue). For rotarymotors, it has the following equation:

${{Pole}\mspace{14mu} {density}} = \frac{N_{p}}{\pi \; D_{AG}}$

where Np is the number of poles, and D_(AG) is the diameter of theairgap. For the case of a linear motor, the denominator of this functionwould be replaced by the length of the carrier along the direction oftranslation.

For distributed windings, the number of slots will be N×the number ofpoles where N is a multiple of the number of phases. So for a 3 phasemachine N could be 3, 6, 9, 12, etc. For concentrated windings, thenumber of slots can vary but must be a multiple of the number of phases.It does not depend on the number of poles, except that certaincombinations of slots and poles will yield higher torque and betternoise-reduction or cogging-reduction characteristics. The minimum numberof slots for a given number of poles should not be below 50% to obtainadequate torque.

Conductor volume may be used to refer to the slot area per length of asingle stator. The slot area is the area of a cross-section of a slot inthe plane which is orthogonal to the teeth but not parallel to the planeof relative motion of the carriers. In an axial motor, this plane wouldbe perpendicular to a radius passing through the slot. The slot areaeffectively defines the maximum conductor volume that can beincorporated into a stator design, and it is usually a goal of motordesigners to have as high a fill factor as possible to utilize all theavailable space for conductors.

Since maximum conductor volume in a stator is defined in terms of slotarea, any stator referred to as having a maximum conductor volume orslot area must have slots and teeth to define the slots. This parameteris defined for rotary motors as:

${{Slot}\mspace{14mu} {area}\mspace{14mu} {per}\mspace{14mu} {length}} = {\frac{N_{s}A_{s}}{\pi \; D_{AG}} = {{slot}\mspace{14mu} {{density} \cdot A_{s}}}}$

where A_(S) is the cross-sectional area of a single slot, or the averagearea of a single slot for stator designs that have varying slot areas.

As a relatively accurate approximation, A_(S) may be calculated as theheight of the tooth, h_(t), multiplied by the average width of the slot,w_(s), such that the equation above becomes:

${{Slot}\mspace{14mu} {area}\mspace{14mu} {per}\mspace{14mu} {length}} = {\frac{N_{s}h_{t}w_{s}}{\pi \; D_{AG}} = {{slot}\mspace{14mu} {{density} \cdot h_{t}}w_{s}}}$

These definitions are size-independent. They can be used to characterizeany motor.

Pole pitch and tooth height may be used to define a specific stator orrotor geometry. Since the parameters are size-independent, measures ofbenefit disclosed herein are likewise size-independent, being written interms of force per area and force per mass, where mass refers to themass of the stator and rotor including any magnets and coils, such thatthe torque and torque per mass for any size rotary motor can be found byan appropriate multiplication factor containing the radius at theairgap. For any two motors of the same airgap diameter, the graphs willhave the same contours for torque as for force/area, and for torquedensity as for force/mass.

A cooling channel is any structure that defines a flow path for coolingfluid, including gas flow or liquid flow, such as passages defined byfins, or unoccupied spaces in slots, or conduits through or around astructure.

Slot depth or post height may also be used as a proxy for the conductorvolume. The post height, also known as the tooth height or slot depth,is a proxy for the amount of cross-sectional area in a slot availablefor conductors to occupy. Although the slots may have a variety ofshapes such as curved or tapered profiles, the slot height is based uponthe closest rectangular approximation which best represents the totalarea of the slot which may be occupied by conductors. This dimensiondoes not include features such as pole shoes which add to the height ofthe tooth without adding substantially to the slot area. For transverseflux motors, the post height is defined as the portion of the post whichis directly adjacent to the conductor coil, perpendicular to thedirection of the coil windings.

A motor series is a set of motor geometries represented by analysis thathave the same construction and winding but with one or two differencessuch as, a range of pole pitches, or a range of post heights.

Number of rotor poles is equal to the number of regions of alternatingpolarity magnetic flux across the airgap. For example, in a surfacepermanent magnet rotor, the number of poles is determined by the numberof alternating polarity permanent magnets. However, poles may also becreated by groups of magnets such as in a Halbach array, byelectromagnets, or by combinations of electromagnets and permanentmagnets. A conductor layer is an electrical conductor formed as a unitthat establishes a conductive path that does not intersect itself whenthe conductor is viewed in plan view. The conductor layer may thus beplaced directly around posts with minimal or no plastic deformation ofthe layer. Each conductor layer occupies a different part of slots atdifferent levels of the slots, for example corresponding to differentaxial positions in an axial flux machine or different radial positionsin a radial flux machine. In some embodiments, a conductor layer may bemade of a material with sufficient rigidity that it can be placed overposts and into slots as a unit, without being individually helicallywound on to the posts.

A continuous stall torque of a direct drive motor is the continuoustorque output at zero speed where the produced heat and dissipated heatreach equilibrium for a given cooling means that is at the maximumallowable electrical conductor temperature.

A concentrated winding comprises individually wound posts or any windingconfiguration that results in the alternating polarity of adjacent postswhen energized. It is understood that not all posts will be the oppositepolarity of both adjacent posts at all times. However, a concentratedwinding configuration will result in the majority of the posts being theopposite polarity to one or both adjacent posts for the majority of thetime when the motor is energized. A concentrated winding is a form offractional slot winding where the ratio of slots per poles per phase isless than one.

The term ‘solid stator’ refers to a homogenous magnetically susceptiblesupport structure functioning as a stator of an electric machine.

Exemplary Radial Flux Electric Machine

FIG. 1 shows a CAD model of a complete exemplary actuator 1010 prototypewith an outer housing 1012 and an inner housing 1014. The inner housing1014 is the fixed (or reference) member, and the outer housing 1012 isthe rotating member. Housings can be made of any rigid material such as,but not limited to aluminum, steel or plastic. The exemplary actuator1010 comprises a bearing/seal 1016 and output mounting holes 1018. Theprototype shown in FIG. 1 has produced a high torque to weight ratio.This is important for applications such as, but not limited to,robotics. The design shown in FIG. 1 has slot density and post heightthat comes within the definition of slot density and post height that isbelieved to provide a benefit in terms of KR, thus being especiallysuitable for use in robotics applications.

FIG. 2 shows a section view of the same exemplary actuator 1010 with aninternal stator 1020 attached to the inner housing 1014 and an externalrotor 1022 attached to the outer housing 1012. The rotor 1022 comprisespermanent magnets 1024 attached to a rotor yoke 1026. The stator 1020comprises stator teeth 1028 attached to a stator yoke 1030. The stator1020 is made of a soft magnetic material such as but not limited tolaminated electrical steel. Solid material can be used for the stator1020 such as but not limited to powdered soft magnetic materials thatexhibit reduced eddy currents and/or reduced hysteresis. Due to theunusually thin flux path cross section of this device which will reduceeddy current losses, solid steel or iron may be used for the stator 1020with acceptable performance in certain lower speed applications. Thesection view in FIG. 2 shows simplified bearings 1016 and no coils onthe stator 1020.

FIG. 3 shows a side view detail of the stator 1020 and rotor 1022 (nocoils shown in this figure for clarity of illustration) FIG. 4 shows aschematic of the entire stator 1020 and rotor 1022 with permanentmagnets 1024 on the rotor 1022 but no coils on the stator 2010.

With a slot density in the range of 0.16 to 0.5 and higher, for example,and considering that it is not unusual for a slot to be about as wide asa tooth, tooth width can be in the order of 2 mm for a 200 mm widemachine. Wider or narrower teeth can be used. An advantage of thinnerteeth is that solid materials may be used with minimal eddy currents dueto the teeth being closer to the thickness of normal motor laminations.A common motor lamination can be in the range of 0.015″ to 0.025″. Thisprototype has performed satisfactorily with a hot rolled steel core.This has advantages for low cost manufacturing. Other advantages ofusing a solid core include the possibility of higher flux densities inmaterials like iron. Permanent magnets 1024 may be adhered to a softmagnetic material rotor 1022. Spacers 1025, shown in FIG. 3, in therotor 1022 are not necessary but may be used to ensure the magnets 1024are assembled at the correct spacing.

FIG. 1 to FIG. 5 show a non-limiting example of a 4:3 post 1028 to PM1024 ratio according to the principles disclosed here for a four phaseconfiguration. In general, for n phases, there may be a ratio of poststo poles of n:n−1, where the number of poles may be the number ofpermanent magnets. A 3:2 ratio may be used (with three phases), orpossibly a 2:1 (with two phases) ratio or a 5:4 ratio (with five phases)or a 6:5 ratio (with six phases) or a 7:6 ratio (with seven phases) andso on. 4:3 has shown to be a ratio which produces high torque and isused as a non-limiting example here. Or there may be n phases, with aratio of posts to poles of n:n+1. Many other post-to-PM ratios andcombinations are possible and can be used according to the principles ofthis device.

The embodiment of FIG. 1 to FIG. 5 has 172 posts, but an electricmachine with the proposed slot density may have greater or smallernumber of posts. A minimum number of posts may be 100 posts to obtainsufficient torque density for some robotic applications. FIG. 5 shows asimplified schematic section view of the stator 1020 and rotor 1022 withschematic CAD model coils 1032 on the posts.

For a 4 phase configuration of an electric machine as disclosed, thenumber of posts may be divisible by 8, with a ratio of 4 posts to 3permanent magnets. The permanent magnets may be arranged with analternating radial polarity.

A high number of posts allows fewer windings per post. In a non-limitingexemplary embodiment, the windings on each posts are only one layerthick (measured circumferentially, outward from the post). This reducesthe number of airgaps and/or potting compound gaps and/or wireinsulation layers that heat from the conductors must conduct through forthe conductors to dissipate heat conductively to the stator posts. Thishas benefits for heat capacity (for momentary high current events) andfor continuous operation cooling. When direct cooling of the coils bymeans of gas or liquid coolant in direct contact with the conductors, alow number of circumferential layers, and for example a singlecircumferential layer of wire on a post, combined with high slotdensity, results in a very high surface area of the conductors (relativeto the volume of the conductors) exposed to the cooling fluid. This isbeneficial for cooling the conductors and is one of many exemplary waysto take advantage of low conductor volume of an embodiment of anelectric machine. A single row (or low number of rows) of coils perposts also reduces manufacturing complexity allowing for lower costproduction. In another embodiment, the windings of each post are twolayers thick.

Exemplary Linear Electric Machine

In an embodiment, such as shown in FIG. 6, an electric machine may bebuilt with a stratified construction which allows main components to befabricated from, for example, sheet stock of conductor material such as,but not limited to, copper, and insulator materials such as, but notlimited to, hard anodized aluminum, with high speed and low costmanufacturing processes such as, but not limited to, stamping or fineblanking. Instead of winding conductor wires around posts, the conductorcircuits may be stamped and then assembled in layers. If insulatorlayers are used alternately with each conductor layer, the conductorlayers may, in some configurations, be assembled without insulationcoating. Alternately, conductor circuit layers can be coated withinsulation before assembly for additional insulation effectiveness, orto eliminate the need for separate insulating layers.

Insulating layers can be of many different types of material. Aluminumis a material which can be stamped or fine blanked and then hardanodized. Hard anodized aluminum provides high voltage insulation andexcellent heat conduction away from conductors. It also providesexcellent structural integrity. Conductor and insulating layers can befixed together with a number of possible adherents including but notlimited to, epoxy, potting compounds, thermally activated adhesives, andthermoplastic adhesives.

Non-electrically conductive (or insulated electrically conductive)materials may be used on the same strata as the conductive layers toprovide structural integrity and heat sink/dissipation qualities. Thesenon-filled layers in the slots between conductor layers can also be usedto provide a flow path for a cooling gas or liquid so that the openslots form conduits. Cooling fluid may also be used as an air or liquidbearing medium. Many different materials may be used for spacer layersincluding, but not limited to anodized aluminum, Torlon™ (a reactionproduct of trimellitic anhydride and aromatic diamines), phenolic, or acomposite material such as, but not limited to a metal matrix composite.

Each conductor may be a layer. Layers may be made up of one or moresections. A section can be, for example, an entire length of a linearmotor, or a complete circumference of a rotary motor, or it can be twoor more lengthwise sections of a linear motor or two or more angularsections of a rotary motor. Each layer in each section may be aconductor circuit for only one phase. In a common electrical machinewith wire windings, the conductor wire is helically wound and overlapsother wire in that phase and/or wire from other phases. This type of3-dimensional wire winding configuration cannot be fabricated with asingle layer per phase because a simple layered assembly does not allowthe interwoven or helically overlapping construction that typical postwinding requires.

A wiring may be used to create a poly-phase motor with each adjacentslot comprising conductors from a different phase or differentcombination of phases than an adjacent slot. This has a number ofadvantages which include simplified manufacturing for reduced cost andthe ability to provide very effective cooling as described below.

The conductor manufacturing methods disclosed are especially effectivein constructing devices with high slot density, as they may replace highprecision wire winding.

A single layer per phase winding in an embodiment may provide aconductor in two adjacent slots and then skipping one or more slots(depending on the number of phases, for example) such that a layerexists in two adjacent slots followed by one or more slots with noconductors on that layer from that phase. Thus, in an electric machinewhere electromagnetic elements of a carrier comprise posts, with slotsbetween the posts, one or more slots are without an electric conductorat a level in the one or more slots corresponding to a location of anelectric conductor in an adjacent slot.

Conductor Layers with Openings

In some embodiments, the disclosed electric machine not only provides ahigh cross sectional area for fluid flow, it provides a consistentlydistributed airflow channel pattern which ensures that every conductoris in contact with the cooling fluid for close to half of its length. Inother words, in an embodiment, there are never more than two layers ofconductor layers contacting at a time. The sequence vertically in a slotmay be for exampleconductor-conductor-space-conductor-conductor-space-conductor-conductor-space.This means that one side of all conductors is always in contact with thefluid in the cooling channels that is created by the missing conductor.This evenly distributed cooling channel array assists in achievingsufficient heat dissipation to compensate for the higher heat productionthat results from a reduced conductor volume.

Some embodiments of an effective cooling channel spacing pattern includeoverlap of the end turns of a conductor combined with offset of thephases combined with a gap at the end of each of the posts to allowtangential airflow at the end of each post. With these details, theairgaps are consistent, fewer (larger) channels are avoided, theconductor surface area is increased and are no stagnant airgaps due tono post-end tangential conduit.

In an embodiment, there may be two slots in a row with a conductor froma phase followed by p minus 2 slots with no conductor from any phase onthat layer (with p being the number of phases). For three phases thatwould be two slots with a conductor from a phase followed by one slotwith no conductor from that, or any other, phase. With four phases itwould be two slots in a row with a conductor from a phase followed bytwo slots with no conductor from that, or any other phase on that layer,and so on. No conductor from that or any other phase means there is anair space or a space that can be filled with potting compound and/or afiller material such as a heat extracting insert.

With a three phase configuration, as a non-limiting example, twoadjacent slots will have a single layer with a conductor from a firstphase in a first and second slot followed by a third slot which will nothave a conductor on that layer. This pattern repeats to provide a singlelayer of winding to provide a conductor on both circumferential sidesfor every first of three posts. On another layer, a second phase circuitexists on a single layer and has a conductor from this second phase inthe second and third slot followed by a slot that will not have aconductor from any phase on that layer. A third phase is on anotherseparate layer with conductors in every third and first slot but noconductor from any layer in every second slot.

A layered construction permits scalable construction from micro/MEMSmotors all the way up to motors that are 10 meters or more in diameter.Layered construction allows components to be deposited with additivemanufacturing processes, or to be assembled with each conductor and/orinsulator component and/or spacer layer being pre-fabricated from asingle or multiple parts.

This winding configuration may be done with a bendable wire conductor oneach layer (which is only helically wound on two posts to connect to thenext layer, for a non-limiting example). Or this conductor configurationcan be assembled from pre-fabricated conductor layers so that little orno bending of the conductors is required during construction andassembly.

Skipping slots has the perceived detriment of reduced slot fillpercentage. However, this missing conductor in periodic slots can beused as a cooling channel to allow direct cooling of a high percentageof the surface area of the conductors and/or insulating layers and/or EMposts. The cooling channel or conduit may be provided with a flow ofcoolant. The missing conductor in periodic slots can be used as an airchannel so as to reduce the weight of the device.

The ability to form the conductors before assembly and to not requirebending of the conductors, is also suited to the use of super conductorswhich are typically less malleable than copper wire. The high surfacearea that is available for coolant contact is also suited to the use ofsuperconductors to keep the conductors below the necessary temperaturefor super conductivity, if using DC currents and superconductors. Theuse of low temperature coolant can also make conventional conductorslike copper and aluminum more efficient by reducing their electricalresistance. Embodiments of the layered conductors are also suited tomaintaining copper or other conductor materials at an artificially lowtemperature for increased efficiency in certain applications.

Stator of Linear Electric Machine

A non-limiting simplified exemplary embodiment of a stator 1058 of alinear electric machine is shown in FIG. 6. The design shown in FIG. 6may comprise an upper insulating layer 1034, a lower insulating layer1034, and a stack of conductor layers 1040, 1042 and 1044. Variousnumbers of conductor layers may be used. Posts 1036 may extend throughopenings 1035 in the insulating layers 1034. Connections 1046 may beprovided to a source of electrical excitation. For each layer 1040,1042, 1044, a separate layer may be provided.

The simple construction of the stator 1058 is evident from the lownumber of easily manufactured components. An insulating layer 1034 canbe made of a non-electrically conductive material or insulatedelectrically conductive material and may be for example made of hardanodized aluminum. It may be punched or fine blanked, and then chemicaletched to remove sharp edges (important to achieve high insulatingvalues at edges when hard anodized) and then hard anodized. The layer1034 is, in this non-limiting exemplary embodiment, 0.5 mm thick, butthe electric machine of FIG. 6 can have a range of dimensions. Theinsulating layer 1034 has rectangular cut-outs 1035 for the EM posts1036 (although other shapes for posts 1036 and post cut-outs 1035 can beused with various effects, and serves to precisely position the posts1036 during assembly). If the insulating layers 1034 are electricallyconductive (even if they have an insulated coating) it is important, forsome applications, that there be no electrical connection around anysingle post within the either layer 1034. For this reason, a cut 1038 isprovided between each slot to break potential eddy current circuit. Thisslot can be punched or blanked or cut at different points in theprocess, such as with a laser before, during, or after assembly. Theminimum thickness of an electric conductor may be >75% of the maximumthickness of the conductor layer. The minimum thickness of the electricconductor may be >50% of the maximum thickness of the conductor layer.This allows for punching and minimal thinning of the conductors atcross-over points. The >50% provides for the gaps to still be necessary.The method of manufacture may comprise punching or stamping a conductorlayer from a constant thickness material and placing the conductor layerinto the slots. The resulting conductor layer may have a variablethickness.

The EM posts 1036 may be made of a soft magnetic material such as butnot limited to, steel or powdered iron or other type of soft magneticmaterial. The conductors 1040, 1042, and 1044 may be made of copper (orpossibly aluminum or super conductors for some applications) and can beformed or punched or fine-blanked and then coated with an insulatinglayer (not shown) such as, but not limited to, coatings that are commonto wire conductors. Surface connection vias 1046 are assembled with therest of the layers or are drilled and added afterward, if needed.

The stator 1058 is assembled by hand or machine, and then may be clampedbetween two flat surfaces and potted with a potting compound. During thepotting process, the top and bottom mold plates can be retracted enoughto allow wetting of all surfaces before being brought axially togetheragain into contact or close proximity. The lengths of the posts 1036 maybe used to position the upper and lower potting mold parts (not shown).

If internal cooling is desired, the potting compound is removed from theopen slot sections such as by allowing gravity to remove pottingcompound from the large gaps, or by pushing air through the device topush the potting compound out of the cavities.

FIG. 7 shows an isometric view of the stator 1058 in FIG. 6 (with nopotting compound or insulating layer shown on the conductors). Thisnon-limiting exemplary embodiment has one conductor per phase persection (which is the complete linear actuator stator 1058, in thisexample.) Multiple conductor layers of the same phase can be used in astator section.

FIG. 8 shows a top view of the stator 1058 in the non-limiting exemplaryembodiment of FIG. 6 and FIG. 7 with the upper insulator layer 1034removed, revealing how each of the phase circuits 1040, 1042, and 1044is a single component (and in this case, having identical geometry) thatnearly encircles every first, second, or third of three consecutiveposts 1036. Phase circuits 1040, 1042, and 1044 correspond to phasesone, two, and three, respectively.

FIG. 9 shows phase circuits 1042, and 1044 removed so the circuit shapeof phase 1040 can be clearly seen to nearly encircle every third ofthree consecutive posts 1036 by filling the slot 1037 on either side ofevery third post 1036, and to skip every first slot 1037. The other twophase circuits skip a different slot 1037 and nearly encircle adifferent post 1036.

FIG. 10 is a sectional view of the non-limiting exemplary stator 1058 ofFIG. 6 to FIG. 9. It shows how a conductor is missing from one out ofevery three consecutive slots 1037 in each conductor layer 1040, 1042,and 1044. FIG. 11 is a detail view of the cross section shown in FIG.10.

Layers can be bonded together or fused together or soldered together. Ifsome internal layers, such as but not limited to the copper layers andspacer layers between the anodized aluminum or other separator layers,are tinned, and if all components or their coatings are bondable by agiven solder compound, the parts can be assembled and then heated underpressure in an oven to fuse everything together. It is important, ifpre-tinning with solder is used, that the separation layers are notcoated so there is no conductor layer-to-layer conductivity.Alternatively, a thermoplastic resin can be used to coat the parts andthey can then be assembled and heated in an oven under enough pressureto ensure the correct axial and other dimensions. An epoxy or otherhardening adhesive can be used during or after assembly to adhere andpot the components. If airflow channels are included in the design,potting can be followed by blowing the adhesive out of the largechambers before the epoxy hardens. An advantage of a pre-preg or soldertinning process which provides a thin and consistent coat of adhesive orsolder, is that the airflow channels may not need to be purged. Only theclose fitting surfaces will adhere to each other. Any number of posts orpermanent magnets may be used.

FIG. 12 to FIG. 21 show a non-limiting linear motor embodiment with apermanent magnet (PM) carrier 1056 and encoders, showing in sequence theremoval of the top layers and revealing underlying layers. There aremany options for encoders that are well known to a skilled person. Inthis example a mini-coil at the end of the posts is used as an eddycurrent sensor, though care must be taken to ensure necessary precision.It is energized with a high frequency signal that generates eddycurrents in the PM magnet coating and/or material between the magnets.The change in eddy currents is used to read position changes. FIG. 12shows an isometric view of a non-limiting exemplary linear actuatorembodiment of an electric machine. FIG. 13 is the actuator of FIG. 12with internal lines shown. FIG. 14 shows the upper permanent magnetcarrier backiron 1048 removed.

FIG. 15 shows an upper permanent magnet carrier plate 1052 and most ofthe upper PMs 1050 removed revealing air cooling discharge holes in theinsulator layer between the PMs and the slot in the spacer between thePMs to prevent eddy currents from circling the posts 1036. Also revealedis the air-core inductive sensor 1054 which can be manufactured on a PCBand added to the rest of the components during assembly. The inductivesensor 1054 can be used to sense the position of anything electricallyconductive on the PM carrier 1056 such as the aluminum between the PMs1050 and/or the electrically conductive coating on the PMs 1050. Thissensor can be used to determine relative linear and/or axial positon ofthe stator 1058 and PM carrier 1056. FIG. 16 shows all PMs 1050 removedand top insulator plate 1034 removed. FIG. 17 shows the electricalconnectors 1062 removed and the top spacer layer 1060 removed. FIG. 18shows the top phase circuit conductor 1044 removed and the secondinsulator layer 1034 removed revealing the air inlet for the internalcooling channels. FIG. 19 shows the second spacer layer 1060 removed andmost of the posts 1036 removed. FIG. 20 shows the upper air core sensor1054 removed and the second phase circuit 1042 removed and thestructural cylindrical spacers 1064 and the rest of the posts 1036removed. FIG. 21 shows the third phase circuit 1040 and the bottomspacer layer 1060 removed, revealing the lower air core PCB insert 1066and the lower insulator layer 1034.

The exemplary embodiment in FIG. 12 to FIG. 21 can be configured withmultiple layers of stators 1058 and/or PM carriers 1056 with PM carriers1056 on both axial ends of one or more stators 1058 or two or morestators 1058 on the axial ends of one or more PM carriers 1056. Only thestator 1058 and/or PM carrier 1056 at the axial ends require a backiron.

Conductor Layers for Exemplary Axial Flux Motor

FIG. 22 shows the conductor circuits 1044 (only one layer is shown inthis figure) and posts 1036 and potting compound ring 1068 for anon-limiting exemplary embodiment of an axial flux, rotary stator 1070according to an embodiment of an electric machine. FIG. 23 shows adetail view of the stator 1070 in FIG. 22 with mounting holes for thestator to attach to another stator disk and/or a fixed or moving memberto be actuated or to actuate from.

FIG. 24 shows the potting compound ring 1068 removed from an axial flux,rotary stator 1070 with three phases and one conductor circuit perphase. In this embodiment, the conductor members 1040, 1042, and 1044are each a single circuit for a complete 360° with an IN and OUTconnection 1046 for each of three phases. The conductors 1040, 1042, and1044 may be for example made of hard anodized aluminum which mayeliminate the need for separate insulator layers between the conductors1040, 1042, and 1044, or the rotor (not shown).

FIG. 25 is an isometric view of the three phase circuits 1040, 1042, and1044 with soft magnetic material posts 1036 positioned by the aluminumcircuits 1040, 1042, and 1044 (and/or an assembly fixture) duringassembly. There is enough overlapping aluminum that for certainapplications, the aluminum circuit 1040, 1042, and 1044 and post 1036cross matrix construction may be strong enough to reduce or eliminatethe need for other structural components like end plate disks. With thisconfiguration, the extra volume of aluminum that can be fit into thesame space as the FIG. 15 stator may allow the aluminum to providesimilar resistance to copper that must be insulated between thickerlayers. Copper can also be used in this way with fewer or no insulatinglayers, but copper insulation tends not to be a tough as aluminumanodizing.

FIG. 26 is an exploded view of FIG. 25 showing the simplicity of thecircuit 1040, 1042, and 1044 shapes, all of which can be symmetrical andsimply rotated relative to each other by one or more posts 1036 as longas other layers do not nearly encircle the same post 1036 as anothercircuit.

FIG. 27 shows a close up view of just the second conductor layer 1042with the posts 1036 FIG. 28 shows a detailed view of just the aboveconductor layer 1042 to show the overlapping sections along the ID,which are for structural integrity to increase the bond area between theconductor layers FIG. 29 is a top view detail of a single stator circuit1044.

As is made possible by embodiments of this stratified conductorconstruction, the cross sectional area of the end turns may be forexample greater than the average or max cross sectional area of theconductors in the slots. This reduces the resistance in the end turnsallowing them to run cooler than the slot portion of the conductors andto therefore act as heat sinks to increase the heat capacity of theconductors to increase the ability to operate at very high currentdensities for short periods of times such as during emergency stops oreven during normal operation during high accelerations. Furthermore, thegreater surface area of the end turns as compared to the slot portions(slot turns) of the conductors provides a cooling fin effect that ishighly effective due to the low heat flow resistance from the slot turnsto the end turns as a result of them being of the same component and ofa high conductivity material such as copper or aluminum. Cooling theseend turn “cooling fins” can be done with any number of liquid or gascooling means.

Exemplary Axial Flux Electric Machine

An embodiment may comprise individually controlled stator sectors, whereapart from producing torque a secondary purpose of the controllers forthe said stator sectors will be to keep the rotor alignment with thesaid sectors, and to possibly eliminate the need for rolling and/orsliding contact bearings altogether. Each section may comprise anindividual multiphase BLDC motor driver. Considering an embodiment witha hollow disk shape like the multi-sectional actuator 1082 shown in FIG.30 one can argue that to some degree every arc sector 1074 must act moreor less like a linear actuator (illustrated in FIG. 31), and so long asevery linear actuator is maintaining its linear (in this casecircumferential) motion or position, each corresponding section of therotor at a given moment will be positioned circumferentially, such thatthe stator and rotor will be held coaxially. It is clear from thedrawing that every stator sector 1076 is only responsible for aprimarily tangential force that can make the corresponding sector 78 ofthe rotor move back and forth tangentially. Even if the stator and therotor are not mechanically coupled with a bearing, the possibility ofmaintaining axial alignment by properly commutating individual sectors1074 is real. One could say that the proposed idea is in a way acombination of torque producing device, and a self-aligned dynamicmagnetic bearing.

An embodiment of an electric machine may be used with a long lever, suchas a robotic arm, with a weight at the end, mounted horizontally on therotational part of the actuator 1082 as shown in FIG. 32. If theactuator is mounted vertically, that is with a horizontal axis, therotor assembly will experience a downward force 1080 and the individualsectors 1084 and 1086 that are diametrically opposed on the horizontalaxes will experience a slight vertically downward displacement. Anencoder at each of the stator sectors will register this displacementand the motor driver and controller will shift the power input to thosesectors to maintain the correct stator-to-rotor tangential alignment ofthose sectors. This will create a vertical lifting force 1088 to counterthe vertically downward force on the arm, and the rotor will, therefore,be maintained coaxially within a predetermined tolerance by the activecontrol of the individual sectors. This is demonstrated in FIG. 32. Allother sections are creating torque as they would normally do. To thecontroller that is simply an increase in force (torque) in one of twopossible directions, and because it is only one of two it won't be acomplicated addition to the driving algorithm to any existing motordrive.

Winding Construction for Exemplary Stator

FIG. 33 to FIG. 37 show a schematic of a three phase non-limitingexemplary stator winding construction with six layers 1040, 1041, 1042,1043, 1044, and 1045 making up a stator for which a top view if shown inFIG. 33. The stator is divided into 1010 sectors, each of which containsa stator winding construction section 1090. Each sector may be forexample controlled by a separate motor controller (not shown) based onthe encoder feedback at each sector which reads the circumferentialposition of the PMs 1050 on a PM carrier 1056 relative to each sector.Controlling each sector separately allows the radial forces to becontrolled by the CPU such that the rotor and stator can be activelyheld concentric by magnetic forces. The effect will be that of an activemagnetic bearing in the radial direction. A detail of the windings isshown in FIG. 34. FIG. 35 shows an isometric view of a single section1090 of the stator winding in FIG. 33. FIG. 36 shows just the topmosttwo layers 1044 and 1045 which are both in the same phase and connectedwith a through-layer via; just the lower layer 1044 of the two conductorlayers is shown in FIG. 37.

Exemplary Axial Flux Electric Machines

Many embodiments are possible. One exemplary embodiment is shown in FIG.38, as an internal stator stack of four stator disks 1092 that allowsthe external rotor stack of five rotor disks 1094 to spin a fullrotation. Another exemplary embodiment is show in FIG. 39, with anexternal rotor with 5 disks stacked together around four stator disks.The stator disks 1092 are fixed together with an ID ring member 1096 andthe fixed tabs 1098 and output tabs 1100 on the stator disks 1092 androtor disks 1094, respectively, allow in-line actuation with very thinaxial dimension. For additional torque, more stator and rotor disks canbe added.

A single or double or other phase array of posts can be constructedaccording to the principles of this device with one or more layers ofconductors. This configuration of an embodiment of an electric machinecan allow simplified control of a linear or rotary or other motorconfiguration, such as, but not limited to a linear motor to control arobotic finger joint.

Exemplary Robotic Joint with Electric Machine

FIG. 40 shows a schematic section of a non-limiting exemplary embodimentof a two-joint robotic finger 1122 using embodiments of an actuator orelectric machine 1102 formed of a first carrier 1104, and a similaractuator 1116. This actuator can be, but is not limited to, a singlephase linear actuator which has multiple poles but only one phase and istherefore not commutated and generates adequate force that a suitablylow mechanical advantage of the actuator (acting through a cable orstrap or linkage etc.) can produce adequate torque and rotation of thejoint to which it is attached. In FIG. 40, an actuator 1102 has a stator1104 that is fixed to the phalanx 1106 and a PM carrier 1108 that isfixed to a cable or strap 1110. The cable 1110 is fixed at the otherend, to a pulley or other member 1112. The pulley 1112 is fixed to thehand member 1114. When the stator 1104 is energized, in one polarity, itallows the phalanx 1102 to rotate in the clockwise direction as a resultof a CW spring (not shown) acting between the hand member 1114 and thephalanx 1102 which pulls the finger straight, relative to the handmember 1114, when the actuator 1102 is extended. When the oppositepolarity is applied to the stator 1104, the cable 1110 is drawn towardthe stator 1104, and so the phalanx 1102 will rotate in the CCWdirection.

A second stator 1116, is fixed to the second phalanx 1118 and actuates acable 1120 that is fixed to the pulley 1112 that is fixed to the phalanx1102. Stators 1104 and 1116 can be driven by the same and/or differentmotor controllers.

Stator 1104 could also be located in the hand member 1114, or anadditional actuator 1104 could be located in the hand member and couldact on the phalanx member 1102 to cause rotation. An actuator fixed tophalanx 1102 can also produce torque and/or rotation of phalanx 1118instead of or in addition to stator 1116.

Two views of a non-limiting example of a robot gripper with threefingers 1122 using an actuation of each joint as described above isshown in FIG. 41. Many different configurations of a gripper using theseor other actuation configurations of an embodiment of an electricmachine are possible.

Exemplary Magnet Configuration for Electric Machine

FIG. 42 illustrates an embodiment of alternating polarity magnets 1050on either side of a layered arrangement of electrical conductor layers1140 to 1143 with posts 1136 seated in insulating layers 1134. Thisillustration shows an axial flux embodiment, which may be either rotaryor linear.

The layered actuator of FIG. 42 may be manufactured by any of themethods in this disclosure, such as, but not limited to using PCBmanufacturing techniques, or an assembly of pre-fabricated components.To reduce the current required to produce a given linear force, morethan a single layer of electrical conductors may be used. Each layer1140 to 1143 may have a separate insulator layer between it and the nextlayer, or each conductor layer can be insulated individually (similar toconventional wire insulation) before or during the assembly process so aseparate insulation layer is not needed between the conductor layers.

With a single phase device, for a non-limiting example, as shown in FIG.42, the EM posts are not commutated. A positive or negative current isapplied to the single phase to create a force and/or movement of the PMcarrier in one direction or the other. The approximate total travel ofthe output will therefore be the post pitch. An advantage of this deviceis the reduced complexity of the motor controller which only needs toprovide a variable positive and/or negative current to produce movementor force of the PM carrier relative to the stator.

Exemplary Linear Electric Machine for Example for Robotic Finger Joint

For many motion control applications, such as finger joints or otherdevices in robotics or motion control, a small amount of movement can bemechanically amplified to accomplish the required task, such as with acable and pulley pulling on a cable “tendon” such as in a human fingeras illustrated in FIG. 40 and FIG. 41. An adult human index finger, forexample, requires approximately 18 mm of linear tendon movement for thefull range of motion of all three joints. If each joint on a roboticfinger is controlled by a separate linear motor and tendon, the totaltravel of each actuator, to replicate a human finger joint motion, wouldbe ˜6 mm. If the mechanical advantage of the robotic tendon was reducedto ½ of the human finger, it would only require 3 mm of total actuatormovement at each individual actuator at each joint to achieve the rangeof motion of a human finger joint.

FIG. 42 shows a simplified cross section of a non-limiting exemplaryembodiment of a four layer single phase actuator with a linear array ofPMs on both axial ends of the array of EM posts. The arrows in FIG. 42indicate the forces on the PMs (which are fixed to a moveable PMcarrier—not shown in FIG. 42). The force on the PMs will be to the rightat the shown EM polarity and to the left at the opposite EM polarity. Byusing a variable current, such as with a PWM signal, this force will beproportional to the current. If the post spacing is ˜3 mm, then fingeractuation of a generally human-sized finger joint can be achieved.

The compactness of this construction may even allow an actuator for eachjoint to be located in the next upstream or downstream arm or fingerphalanx. This eliminates the need for a flexible cable sheath and allowsdirect acting of the cable/tendon on the joint in line with the actuatorplane of movement. For more powerful finger or other componentactuation, a cable with a flexible housing can be used to situate theactuator for one or more joints remotely, such as in the forearm of arobot, where more room is available.

An advantage of this actuator system is that a force can easily beapplied to a joint (as compared to a commutated magnet array in amulti-phase and linear or rotary motor which must have a feedback systemto achieve controlled force application). The force generated by theactuator will be proportional to the current, so a force feedback sensormay not be necessary for many applications. An encoder may not be neededfor many applications. This configuration may be suitable for many otherrobotic or motion control requirements where a limited travel linearmotion will provide the required force and/or movement.

Applying the same variable current to all actuators in a finger, witheach actuator controlling a different joint, a highly compliant fingerassembly can be achieved where the finger will conform to a givenpayload at each joint with the option of only a single current controlfor the whole finger. Separate current control of individual actuatorswill allow individual joint control.

Layered Construction of Exemplary Electric Machine

The above magnet configuration in FIG. 42 is shown in the assembly inFIG. 43 through FIG. 52 with a layer removed in each subsequent figureto show the layered construction.

Insulator layers 1134 may be made of any non-electrically conductivematerial, or with an insulating coating on a conductive material such asaluminum. Anodized aluminum may be used because of its high heatconductivity. For low frequency applications such as a finger actuator,eddy currents are not a concern so an electrically conductive statorlayer does not need any breaks around the posts.

FIG. 43 shows the complete actuator 1156 of FIG. 42 with PM carrierbackiron 1148, upper PM carrier 1152, lower PM carrier 1157 and stator1158. FIG. 44 shows the actuator 1156 with PM carrier back-iron 1148removed. FIG. 45 shows stator 1158 with PM carriers 1152, 1157 and PMsremoved. FIG. 46 shows the actuator 1156 with top insulator layer 1134of stator 1158 removed showing four layer single phase single circuitconductor, with connectors 1124, 1126 for connecting to a single phasecurrent source (not shown).

FIG. 47 is a detail view of via connector 1146 between conductor layers1141 and 1142 and IN and OUT connectors 1124 and 1126 formed of poststhat connect to the electric conductors of the conductor layers 1140 to1143 FIG. 48 is a detail view of via connectors 1146 between layers 1140to 1143 at opposite end of the stator 1158 to IN and OUT connectors 1124and 1126 shown in FIG. 47.

FIG. 49 shows a top conductor layer 1143 and a dozen EM posts 1136removed. FIG. 50, FIG. 51, and FIG. 52 show, respectively, the actuator1158 with electric conductor layers 1143 removed, layer 1142 removed,and showing only layer 1140.

There need not be separate insulator layers between adjacent conductorlayers in the non-limiting exemplary embodiment in FIG. 42 to FIG. 52.This is possible if the conductor layers are coated with an insulatorbefore or during assembly/construction. The use of insulating layersbetween conductor layers would eliminate the need for insulating theconductors.

The above can be configured with two or more stators on either axial endof one or more PM carriers. PM carrier can have any type of PM magnetand can be configured with a Halbach array or pseudo Halbach array (withPMs polarized in the direction of carrier motion with steel between themto provide flux linkage). The stator and “rotor” may both be energizedto reduce or eliminate the need for permanent magnets. Any number orgeometry or size of posts and PMs or other components may be used.Manufacturing techniques include PCB manufacturing techniques withconductive traces used for coils and posts assembled with pick-and-placeequipment. Mems machines can be built with these techniques in verysmall sizes, subject to a lower limit where electrostatic forcesdominate electromagnetic forces. Larger motors or actuators orgenerators can use a pre-fabricated conductor process as described forother embodiments in this disclosure.

Exemplary Electric Machine with Coils on Both Carriers

An example of an electric machine is shown in FIG. 53, FIG. 54, and FIG.55, with coils on both carriers. Like the other electric machinesdisclosed here, the electric machine of FIG. 53 may have the disclosedslot density and post height or conductor volume. The example given isfor radial flux, but the design principle could be used for axial fluxand linear electric machines. Either the inner carrier 1220 or outercarrier 1222 may be fixed. The stator 1220 is wound with wire, such as,but not limited to copper wire. It can be commutated to vary the currentto individual posts or phases, or it can be energized with variable DCcurrent so the DC electromagnetic posts may be wound and energized tosteer flux from all the PMs 1224 at the same time. This flux steeringredirects the flux from the PMs 1224 from short circuiting through thestator 1220, and causes it to find a lower reluctance path across theairgap to the rotor 1222. The rotor 1222 can be passive (but only if thestator coils are commutated) or it can be commutated with coils 1232around the posts 1227 (if the stator is commuted or energized with DCcurrent). The result is an embodiment that has reduced or no flux acrossthe airgap when the coils on the stator 1220 and rotor 1222 are notenergized. This reduces or eliminates cogging and back EMF (alsoreferred to as damping force) when the rotor is backdriven when thecoils are not energized. Backdriveability is a benefit for manyapplications including robotics and wheel motors. This embodiment canstill act as a generator but requires energizing of the stator coils.

In FIG. 53, FIG. 54, and FIG. 55, there are 1168 posts on the stator1220 and 1140 posts on the rotor 1222 (although many differentcombinations of stator posts and rotor posts can be used). The outerdiameter (OD) of this nonlimiting example is approximately 8.4″ and theaxial length is 1″. The stator may be made of a soft magnetic steel andcan be made from a solid piece of ferrous material or laminatedmaterial. The rotor 1222 may be made of a soft magnetic steel and can bemade from laminated material or from a solid piece of ferrous material.The wires may be copper or aluminum but can be made of any kind ofconductor including foil or square wire or superconducting material.This size of actuator is considered, by the inventor, to be well suitedto a shoulder or elbow joint of a human sized robotic arm. The housingis not shown here but can be of any geometry which serves to keep thestator 1220 and rotor 1222 concentric and aligned. FIG. 53 is anisometric section view showing the stator with 1168 posts with coils1232 comprising a single layer of wire per post 1227, 1228, and apermanent magnet 1224 contacting each post near the OD of the stator1220. It also shows the array of 1140 rotor posts and coils 1232 maycomprise a single layer of winding on each, and backiron 1230 of thestator 1220.

When no power is supplied to the stator coils 1232, the flux from thePMs can “short circuit” through the stator so there is reduced or noflux that jumps across the airgap. This reduces or eliminates thecogging torque when the coils are not energized. When the inner coilsare energized, for example with a DC current, a portion of the flux fromthe PMs 1224 is steered toward and across the airgap to the rotor posts(along with the stator post flux). The greater the current in the statorcoils, the higher the flux density in the airgap.

The stator posts 1228 can be wired together into a single circuit thatis all energized at the same time. The rotor posts may be wired andenergized in phases (5 phases in this example, but other numbers ofphases can also be used) and then commuted by moving the pattern ofpolarities along sequentially. In this example, the rotor post polarityis S N S N S S N S N S S N S N S S N S N S etc. Other polarityconfigurations may be used for example a repeating pattern of NS. Thefirst or second set of adjacent S poles can also be turned off.Sinusoidal or other current profiles can also be applied to each postfor commutation. In this example, the rotor and stator are wound with 24gauge wire and energized with 20 amps. The stator and rotor are 0.5:wide. The whole assembly weighs approximately two lbs and has a torqueat 20 amps of approx. 50 Nm. Higher current is believed possible forshort periods of time to achieve higher torque. Wider stators willproduce higher torque.

When provided with housings 1212, 1214 as shown in FIG. 54, heatdissipation from coil to housing may be shared between the inner housing1214 and outer housing 1212.

Exemplary Electric Machine with Halbach Array of Magnets

FIG. 55 shows an embodiment of an electric machine using a Halbach arrayof permanent magnets on an inner stator. Halbach arrays are known foruse as permanent magnets in an electric motor. This is an effective wayto use permanent magnets and analysis shows that it has a similar toqueto weight ratio of the flux steering stator described in FIG. 53 andFIG. 54. Permanent magnets, have a lower flux density than steel so themaximum torque possible for a Halbach array embodiment is expected to belower for a given diameter (and possible stator/rotor mass) than with aflux steering embodiment as described earlier in this disclosure.Advantages of using a Halbach array include a low profile form factorwhich is a significant value for many applications. The short heat flowpath for the conductors which results from high slot density is expectedto provide improved torque density. The Halbach array may be provided onthe stator or rotor, and either may be the inner. In another embodiment,triangular magnets may be used with alternating radial polarity but softmagnetic material triangular flux path connectors between each magnethaving a similar shape and size to the Hallbach magnets. The advantagesof this configuration include lower cost due to half the number ofmagnets, lower tolerance stackup due to being able to connect all of thesteel triangle parts into a single backiron component, and bettersecuring of the permanent magnets due to them being magneticallyattracted to the soft magnetic material rotor backiron.

Exemplary Axial Flux Electric Machine with Inner Bearing and OuterOutput

FIG. 56 shows a cross-section of an exemplary actuator 2100. An outerhousing 2102 is fastened to an outer housing 2104. A stator in two partsor equivalently a first stator 2106 and a second stator 2108 is fixed toeach of the inward facing surface of housings 2102, 2104 by mechanicalmeans such as threaded fasteners, and or with an adhesive or otherfixing method. Rotor 2110 is fixed for rotation with a bearing 2112which holds it concentric and at a fixed axial position relative to thehousings 2102 and 2104.

FIG. 57 shows a detailed cross section view of the embodiment from FIG.56. Permanent magnets (not shown) are mounted in the rotor 2110. Thesection plane goes through a post 2114 on the stator 2106, but thesection plane does not go through a post on the stator 2108. This isbecause in this exemplary embodiment the stator 2108 is rotated by onequarter of a post pitch to reduce the cogging force of the permanentmagnets in the rotor 2110 interacting with the posts on the stators 2102and 2104. Rotating one stator relative to the other serves to cancel outthe somewhat sinusoidal cogging torque produced between the rotor 2110and the stators 2106 and 2108. This effect is demonstrated in FIG. 58,where the first fundamental harmonic of torque 2300 produced by theelectrical wave and the first harmonic of cogging torque 2302 areplotted on line 1 b as functions of rotor position, indicated by thenumbers 0 through 6, with 0 and 6 corresponding to the start and end,respectively, of an electrical cycle. The posts 1 b of stator 2106 andposts 2 b of stator 2108 exert attractive forces 2306 on the rotorpermanent magnets 2124. In this non-limiting exemplary embodiment, thereis a 3:2 ratio of posts to magnets resulting in 2 cogging steps 2308,2310 per stator post. Rotationally offsetting one stator relative to theother by one quarter of a pitch, therefore aligns the somewhatsinusoidal cogging torque 2302 of one stator at 180° out of phase fromthe cogging torque 2304 of the other stator to achieve a beneficiallevel of cogging torque cancellation. Other ratios of stator posts 2114to rotor magnets 2124 will have other numbers of cogging steps and willrequire different offset angles to achieve maximum cogging cancellationaccording to the following calculation.

The number of cogging steps is given by the LCM—Least Common Multiplebetween P the number of posts and M the number of magnets, so for 3:2ratio the number of cogging steps is lcm(3,2)=6

Examples

3:2 ratio—lcm(3,2)=6 cogging steps

24:16 ratio—lcm(24,16)=48

144:96 ratio—lcm(144,96)=288

144:142 ratio—lcm(144,142)=10224

144:146 ratio—lcm(144,146)=10512

The offset angle is found based on the number of cogging steps, so iffor one electromagnetic cycle of 360 electric degrees there are 6 cyclesof cogging which means that the cogging cycle completes at each 360degrees/6=60 electrical degrees.

The 60 electrical degrees correspond to 360 degrees of the coggingmechanical wave. To cancel a wave you need a wave of the same frequencywith the phase shifted by 180 degrees. So 180 degrees of mechanicalphase shift corresponds to 15 degrees of electrical wave, which meansthat the second stator should be shifted its electric phase by 15degrees. If not the total torque instead of 2×TQ, would be 2×TQ×cos(15deg)=2*TQ*0.966=1.932*TQ of one stator.

If the stator shifts by half of the stator pitch, the cogging steps waveshifts its phase by 360 mechanical degrees, which means a full coggingstep that adds the two waves instead of cancelling them. To cancel thewaves the shift has to be done by ¼ of the pitch which corresponds to180 mechanical wave degrees.

As shown in FIG. 58, the ¼ pitch offset comes from the 3:2 ratio, ifthere are 6 cogging steps there should be 6 neutral positions where thetorque is zero.

Positions 0, 2, 4 and 6 corresponds geometrically to half pitch and fullpitch.

0 and 4 corresponds to zero or full pitch.

2 and 6 corresponds to half pitch.

Positions 1,3,5 corresponds to ¼, ¾ and 5/4 of pitch.

FIG. 59 shows an exploded view of the device in FIG. 56. Thisnon-limiting exemplary embodiment 2100 has stators 2106, 2108 (notshown) on either axial end of a rotor 2110. The stators have a backiron2126 with an array of fins 2139 projecting from the back surface, and2144 radially aligned, axially extending posts 2114 corresponding with2144 slots. There are 96 magnets 2124 and the stators 2106, 2108 arepowered by a three phase sinusoidal power from a motor controller. Arange of slots can be used and a range of magnet numbers can be usedwithin the disclosed range. Various numbers of phases can be used; manydifferent wiring configurations can be used.

An exemplary embodiment uses a fractional slot winding with N52permanent magnets. Many different permanent magnets can be used and manydifferent magnetic materials can be used.

Exemplary Axial Flux Electric Machine with Layered Construction

In an embodiment shown in FIG. 59 and FIG. 60, an array of tangentiallymagnetized permanent magnets 2124 are magnetized tangentially in thesequence NSSNNSSNNSSNNS . . . . Such that every first radial flux pathmember 2128 on the rotor 2110 is N polarity at both axial ends and everysecond flux path member 2130 is S polarity at both axial ends. The rotor2110 includes a sinusoidal surface 2116 which can be used in conjunctionwith an encoder such as, but not limited to an eddy current sensor, anoptical sensor, or other sensor to provide radial position of the rotor2110 for the motor controller. Many other types of encoders can be usedwith embodiments of this device. The cylindrical section 2118 of therotor 2110, serves to provide an attachment surface from the rotor 2110to an output, such as a robotic arm, and to provide stiffness to therotor 2110. This cylindrical member 2118 can be one piece with the rotor2110, or it can be a separate component such as, but not limited to analuminum ring which is assembled to the disk by thermal expansion and/orotherwise attached to the disc section of the rotor 2110. Separatordiscs 2120 may be used to seal and contain the conductors 2122 in theslots between the stator posts 2114. If separator discs 2120 are used,they may be of a non-electrically conductive material such as Torlon™ (apolyamide-imide) or other non-metallic material to prevent eddycurrents. The conductors 2122 may be of any construction, includingwires, but may be a layered construction, as shown here. Conductors maybe of any material but may be of copper, or aluminum.

FIG. 60 shows a section view of the device from FIG. 56 with the housing2102 and stator 2106 assembly exploded, the rotor 2110 and magnets 2124exploded, and the housing 2104 and stator 2108 are assembled. An airflowinlet 2132 is shown on the housing 2104 with cross-flow openings 2134,2136 in the separator disk 2120 and the rotor 2110 to allow coolingfluid flow from one side of the actuator 2100 to the opposite stator.

FIG. 61 is a section detail view of housing 2102. The inside surface ofthe housing 2102 has an array of receiving slots 2138 for the array offins 2139 on the back surface of the stator 2106. These receiving slots2138 serve to secure the back surface of the stator 2106 to the housing2102, and also to transmit heat conductively from the back surface ofthe stator 2106 to the housing 2102. The volume between the stator 2106and the housing 2102, and between the receiving slots 2138 may be usedas a fluid flow chamber to draw heat away from the back surface of thestator 2106 and the internal surfaces of the housing. Gas or liquid canbe circulated through this chamber by means of a pump or compressor (notshown). The cooling effectiveness of the disclosed slot geometry allowsfor high performance to be achieved with air as a cooling fluid in manyapplications. The use of air instead of liquid has many potentialadvantages including lower cost and weight and the elimination ofconcerns about leakage in many applications.

FIG. 62 shows the stator 2106 assembled to the housing 2102. In thisexemplary embodiment the stator 2106 comprises an array of axiallyextending radially aligned posts 2114 with a slot density and conductorvolume within the disclosed ranges. An array of fluid ports 2140 isshown on the stator 2106 to provide an inlet or outlet for fluid in thechambers between the stator 2106 and the housings 2102 and 2104.

FIG. 63 shows the stator 2106 assembled to the housing 2102 with thefirst conductor layer 2142 of phase A of the 3:2 stratified conductorconfiguration of an embodiment of an electric machine. Each layer of aphase of this embodiment of the conductors occupies a single axial layeron the stator 2106 with no other conductors from other phases on thatsame layer. A conductor 2142 on a layer occupies two slots 2143, 2145 insequence and then skips a slot 2147 so that a first slot 2143 on a layerhas a conductor 2142 from a phase providing current flow in one radialdirection, a second slot 2145 on that layer has a conductor 2142 fromthat phase providing current flow in the opposite radial direction, anda third slot 2147 on that layer has no conductor. This conductor shapeand sequence of one conductor layer 2142 in one phase is shown in FIG.64.

FIG. 65 shows four layers of conductors 2142 of the same phase with thestator 2106 and conductors from other phases removed for clarity. Axialinserts 2148 connect the end of each conductor 2142 from a phase on alayer with the start of another conductor 2142 from the same phase on adifferent layer.

FIG. 66 shows the conductor arrangement in the exemplary embodiment 2100with one conductor layer 2142 from each phase. The end-turns of oneconductor layer 2142 overlap the end-turns of the next conductor layer144 in such a way as to provide a fluid flow passage 2150 radially(outward in this example but fluid can flow in either direction) betweenlayers in a slot. Stator posts are not shown in this FIG. 66. In FIG.67, the fluid flow channel in every third slot 2147 on the same layer isshown by the dashed arrow lines in three exemplary slots. Every firstpost 2250 on the stator 2106 has a conductor 2142 from phase A on eithertangential side. Every second post 2252 on the stator 2106 has aconductor 2144 from phase B on either tangential side. And every thirdpost 2254 on the stator 2106 has a conductor 2146 from phase C on eithertangential side.

This stratified winding configuration allows radial cooling fluid flowin the spaces between the conductors between the posts, but theend-turns seal the slots from radial access to the channels in theslots. To provide flow to the radial channels 2150, the conductors 2142are pre-formed with an axial flow path 2152 at the end of each of theposts 2114 as shown in FIG. 68. This axial flow path 2152 allows for theradial fluid flow in a channel 2150 in a slot 2147 to flowcircumferentially at the end of a post 2114 and then axially in theaxial fluid path 2152, and then radially outward (or inward depending oncoolant flow direction) in the radial flow channel 2150 on a differentlayer.

This flow path is shown in FIG. 68 where the thick arrow shows theairflow up to the inlet channel 2154 which is radially aligned with apost 2114. The thick dashed arrow shows the radial flow in the inletchannel 2154. The fine dashed line indicates the tangential flow acrossthe end of the post 2114, and then axial flow in the space 2152 at theend of the post 2114. The long dashed line indicates the flow radiallyoutward in the channel 2150 between the conductors 2142. By creating anaxial flow path 2152 at the end of the posts 2114 in this way, thecooling fluid has multiple routes where it can flow tangentially andaxially to connect inlet and discharge air to the radial flow channels2150.

FIG. 69 shows the same flow path with similar arrows. It is important tonote that the post end spaces 2152 allows cooling fluid to enter on onelayer and to flows radially in a channel 2150 on a different layer.

Embodiments of a stratified conductor system may include, radiallytapered conductor in a radially tapered slot to achieve a higher slotfill percentage, the ability to stamp conductors for ease ofmanufacturing, layered construction to simplify and increase theprecision of assembly, the ability to achieve greater consistency ofmanufacturing, the ability to achieve consistent fluid flow channels foreven cooling, and the ability to create a large surface area of coolantcontact with conductors relative to the volume of the conductors formore effective cooling though active cooling means.

Embodiments of a stratified conductor system as shown in FIG. 63 andothers, are characterized by the same thickness of conductor for themajority of a layer and with a variable width that includes a widersection at the end turns with greater cross section perpendicular to thedirection of current flow. The wider cross section at the end turn isbeneficial because it reduces the resistance and heat production of theend turns by a squared effect allowing the end turn to operate at alower temperature than the narrower conductors in the slots. The verylow heat flow resistance between the slot turns and the end turns, alongwith the larger cross sectional area of the end turns, provides a veryeffective heat sink for heat generated in the slots. The larger surfacearea of the end turn (as compared to if the end turns were the samewidth or smaller width as compared to the maximum width of a conductorin a slot) provides increased surface area for cooling fluid interactionif the end turns are actively cooled and/or for conductive heat transferthrough successive layers of electrical conductor end turns axially tothe housing.

Any number of layers may be used with this stratified conductor system.Any number of phases may be used with this conductor system. With allnumbers of phases, the conductor may, for example, fill two adjacentslots with current flow in opposite directions in these slots, and thenskip X-2 slots with “X” being the number of phases. With four phases,for example, each conductor on a layer would skip two slots rather thanskipping one slot as with three phases. With five phases each conductorwould skip three slots and so-on.

Exemplary Axial Flux Electric Machine

A cross sectional view of a non-limiting exemplary embodiment 2156 ofthe device is shown in FIG. 70, with an average airgap diameter of 175mm. A rotor 2158 with 2146 permanent magnets (not shown) correspondingwith 2146 radial flux path members 2160 is rotationally fixed on abearing between two stators 2162 which each have 144 posts 2164 and 144slots. Three phase control is used, although other numbers of phases arepossible. As is shown in FIG. 71 the conductors 2166 from each of thethree phases are located in two equally and diametrically oppositearrayed sections of 24 slots each. The second section in each of thethree phases is wired in reverse current flow direction to the firstsection and each section of a phase is wired in reverse to the phaserotationally adjacent to it. The conductors 2166 can be of conventionalwire but may be a stratified conductor system such as is shown in FIG.70 to FIG. 78. In this embodiment, the conductors 2166 in a phase ineach section alternate radial direction in each adjacent slot in onecircumferential direction; reverse circumferential direction at the endof a section; and alternate radial directions in the oppositecircumferential direction such that the current is always flowing thesame radial direction in all the conductors in a slot, and each slot hasthe opposite current flow direction at a given moment compared to anadjacent slot in that section such that the posts in a section aremagnetized with alternating polarity at a moment energized.

The pattern of the wire for 6 sections of 24 slots each is as shown herewhere “A” indicates the circuit is wired in one direction and “a”indicates that the same circuit is wired in the opposite direction, withdifferent letters designating different phases. Only the first 6 slotsare shown.

Slots Sections 1 2 3 4 5 6 . . . 1 A a A a A a . . . 2 b B b B b B . . .3 C c C c C c . . . 4 a A a A a A . . . 5 B b B b B b . . . 6 c C c C cC . . .

Above is the phase and polarity pattern for one stator. For anembodiment with two stators, and which uses a rotor for example asdisclosed in this document, with the same polarity on both axial ends ofa radial flux path member, the physical structure of the second statorwiring should be mirrored about a plane through the center of the rotor.The current flow, however, should be in the opposite(clockwise/counter-clockwise) direction in axially aligned posts on oneof the stators compared to the other.

The 144:146 size is by no means limiting; a wide range of slot numbersand magnet number is possible.

FIG. 72 shows a section view of a simplified stator 2172 with the startand end connection 2176 phase and polarity for conductors 2174 from thevisible phases using the convention described above.

Due to the very high number of cogging steps of this device, the coggingamplitude is expected to be very low. It is therefore expected to beunnecessary to position the stators at angles to each other as shown inFIG. 56.

Exemplary Cooling Structures for an Axial Flux Electric Machine

Passive cooling may be used for example through conductive heat transferfrom the electrical conductors to the back surface of the statorback-iron of each stator. In the embodiment of FIG. 70 and FIG. 71, thebackiron 2170 may be made of a one-piece material such as solid iron orsteel and may be a low electrical conductivity but high magneticsaturation material such as, but not limited to, a powdered Permendur™49Fe-49Co-2V or another soft magnetic material that can be a non-flatshape. Solid in this context means that the magnetic material of thestator is continuous and free of non-magnetic laminations.

The stator 2162 has an array of cooling fins 2178 on the back face ofthe stators 2162 that increases surface area and provide increasedcooling rates for passive cooling such as by radiative effects andconvective fluid flow. The cooling fins 2178 will also increase theeffectiveness of active cooling such as forcing gas or liquid over thecooling fins 2178. The cooling fins 2178 can also be sealed inside achamber such as a housing (not shown). The cooling fins 2178 shown hereare not radially aligned. This is to create a structural matrix with theradially aligned posts 2164 for increased circumferential rigidity. Theaxial construction and short axial features of this stator configurationmake it suited for construction from powdered magnetic materials. Theposts 2164 and fins 2178 can be tapered in the axial direction tofacilitate press forming or other production methods. The conductors2166 can also be of different widths from the bottom of the slot to thetop of the slot to achieve the desired slot fill at each slot depth.

In the embodiment shown in FIG. 73, the conductor system provides acombination of uninterrupted axial conductive heat flow path 2180 as aresult of greater than 50% width of conductors in slots 2185 and nomissing layers of conductors 2186, and the possibility of radial coolingfluid flow chambers if desired though channels 2182. This can beaccomplished a number of ways according to the principles disclosedhere. In the exemplary embodiment shown in FIG. 73, the conductor 2186on either side of a post 2184 is close enough to post 2184 on both sidesof post 2184 to allow the post 2184 to precisely position the conductor2186 in both circumferential directions and to create a bond 2188between conductor 2186 and the side of the post 2184. This precisionpositioning helps ensure that the gap 2182 is created on the oppositeside of a conductor 2186. This pre-formed narrowing of the conductor2186 and shape which ensures it is off-center and contacting one wall ofslot 2185, helps provide structural rigidity and fluid flow function onthe non-contacting circumferentially facing side.

Another feature of this construction is the gap 2182 on only onecircumferentially facing side of a conductor 2186 in a slot 2185. Thisis to help ensure that potting compound or varnish does not fill thechannels 2182 as would be more likely with two small channels comparedto one large channel. This construction also helps ensure that eachconductor 2186 has a circumferential conductive heat flow path 2190 tothe side of a post 2184.

As a result of the construction shown in FIG. 73, the heat fromconductors 2186 in a slot 2185 have an uninterrupted axial heatconduction path 2180 through the conductors 2186 to the back-iron 2194of the stator 2193, a circumferential heat conduction path to a post2190 to allow a short heat flow path through the post to the back iron2192. From the back surface of the backiron 2196, heat from the stator2193 can be transferred to the housing 2198 conductively as shown inthis figure, or to a cooling fluid, or radiated to another body (asshown in other embodiments).

An embodiment in FIG. 74 has periodic layers 2200 that are the fullwidth of the slot 2203, and periodic layers 2202 that are narrower thana slot 2203. The layers 2202 may be prefabricated to locate on bothsides of every second post 2205. This provides a consistent andrepeatable fluid flow channel 2201 with a minimized possibility ofobstructing the channel with potting compound as would be the increasedrisk if the narrower conductor 2202 was centered. The narrowerconductors 2202 may be axially thicker to match the cross sectional areaof the wider conductors 2200. Conductors 2202, in this configuration canbe narrower than 50% while still providing structural rigidity of theconductors in the slots 2203. The option to use narrower than 50% widthfor a layer allows a larger cross sectional area for a channel 2201 thanthe single thickness construction shown in FIG. 73.

FIG. 75 shows an exploded view of four layers of the embodiment in FIG.74. The wider but axially thinner section of the conductors 2200 areshown clearly here in contrast to the narrower but axially thickerconductors 2202.

If a higher number of turns per post is desirable for an application,multiple layers of thinner conductors 2206 can have the same axialprofile as shown in FIG. 76. This allows a multi-layer thickness fluidflow gap 2208 with the advantage of preventing obstruction of the gapwith the potting compound, or allowing a thicker potting compound to beused without permanently filling the fluid flow gaps.

Multiple thinner layers 2206 can be used in parallel or in series withvarious effects. In an embodiment, thicker layers (not shown) may beconnected in series with adjacent layers at the bottom of a slot, andthinner layers may be connected in parallel at the top of a slot. Thethinner layers in parallel are believed to have the advantage ofreducing eddy currents in the conductors closest to the permanentmagnets during rotor rotation.

All of these embodiments benefit from an axial cooling fluid flow pathat one or both radial ends of a post which result from the radialconductor slot being longer than the stator post which it partiallyencircles, which allows fluid flow in the slots to enter or exit theconductor section on a different layer than the radial flow in a slot.The radial ends of posts define radial end portions.

Variations of these conductor constructions can be combined with othervariations of other embodiments of the present conductor system.

The conductors in FIG. 71 are pre-formed to provide a gap 2169 on oneside of the slot 2167 between the side of the conductor 2166 and theside of the post 2164. This gap 2169 is combined with an axial flow path2168 at the end of post 2164 which allows cooling fluid to flowcircumferentially at the end of post 2164 and then axially along the endof post 2164 through gap 2168, and then radially outward (or inward ifflow is reversed) in the gap 2169 between conductors from two slots 2167on a different layer. The conductor 2166 has a clearance on both sidesof every first post 2164, and is close fitting on both sides of everysecond post 2165.

The electrical connections between axially adjacent conductor layers canbe done a number of ways. Electrical connections may be between axiallyadjacent conductor elements to serially connect the electrical flowpaths of the axially adjacent conductor elements. An embodiment uses theoverlapping surface area of two conductors in a slot at the end of asection to provide a large surface area for soldering (or otherelectrical connection method). The use of two conductors from two layersin a slot allows up to the entire slot length of two layers to be usedas a single conductor. This reduces the electrical resistance enough toreduce the cooling requirement in that slot. This is important becausemaintaining a precision flow channel will be more difficult at asoldered connection so fluid flow may be more difficult to guarantee inhigh production.

A construction that allows double overlapping surface layer connectedconductors in a slot is shown in FIG. 77. The conductors 2218 will becoated or otherwise insulated, such as with paper between layers oranodizing, except for the area in an end slot where two mating surfaces2220 and 2222 from conductors 2218 on adjacent surfaces will beun-insulated and connected together with an electrical conductor.Methods of construction include manual or automated soldering of aconnection at alternating ends of a section as each layer is placed ontop of another layer. Pre-tinning these surfaces will allow this processto be done precisely. Spot welding of these surfaces may allowelectrical connection without adding thickness to the joint and wouldeliminate the risk of excess solder making unwanted contact with othersurfaces. If aluminum conductors are used, they can be hard anodized andthen prepared for tinning (such as by masking during anodizing, and thenthe connection surfaces can be stripped of oxidation in an inertenvironment). While still in the inert environment, the surface can thenbe tinned or coated with solder paste. This protects the aluminumconnection surface from oxidation during storage and assembly. The sameprocess can be used for the end connections 2224. During assembly of asection of conductors 2218, the layers can then all be stacked inside aseparate assembly fixture, or inside the stator (not shown). Applying ahigh current to the conductors for a short time, can create enough heatto melt the tinned solder together, or a reflow oven can be used to fusethe solder or solder paste. After the layers are connected and theconductors are positioned in the stator slots, a potting compound orvarnish, etc may be used to displace all air (or other gas) in thestator slots. To ensure that coolant flow passages are open during use,the potting compound or varnish, etc is removed from the coolant flowpassages by some means including, but not limited to, air flow and/orgravity and/or centrifugal force.

If radial in-slot cooling flow chambers are not implemented in anembodiment, the device of FIG. 78 will still provide the benefits oflarger end-turn circumferential cross sectional area (compared to radialcross sectional area of slot portion) of electrical conductors 2218 toreduce heat production and to increase surface area for cooling and toprovide greater uninterrupted cross sectional area of axially stackedend turns to allow heat flow at lower resistance to the back-iron orhousings (not shown) that is axially aligned with the end turns. Thelarger cross sectional area also provides greater volume in the endturns compared to the same or lower cross sectional area (normal tocurrent flow) in the end turns.

Active cooling of this embodiment can also be done with radial fluidflow, but there are no missing conductor layers so an alternateconstruction may be used to provide consistently sized and spaced radialfluid flow channels. Spacing the conductors axially may be possible andwould expose a large surface area of the conductors to the fluid, butthis would be difficult to achieve a consistent gap and would not bewell suited to thin conductor layers with low stiffness. One or moreconductor layers may be used in a slot with a narrower width thanconductors on other layers and-or one or more conductors may be used ina slot that are the same width but offset circumferentially such thatthe conductors overlap in the axial direction, but are closer to onecircumferential side of a slot than the other. By alternating successiveor periodic layers from circumferential side of a slot to the othercircumferential side of a slot, an uninterrupted heat conduction pathcan be created from the conductor that is furthest from the statorbackiron to the bottom of the slot. At the same time, one or more radialchannels can be created between conductor layers to provide coolant flowacross conductor surfaces in a slot.

In an embodiment one or more conductors in a slot are the full width ofthe slot (minus clearance for insulation and assembly), and one or morelayers in a slot are narrower than the slot so as to create a gap forfluid flow.

In an embodiment one or more conductors in a slot are the full width ofthe slot (minus clearance for insulation and assembly), and one or morelayers in a slot are narrower than the slot and not centered so as tocreate a gap for fluid flow on only one circumferential side of thenarrower conductor.

In an embodiment one or more conductors in a slot are the full width ofthe slot (minus clearance for insulation and assembly), and one or moreconductors in a slot are narrower than the slot and thicker than thewider conductors such that the cross section of all conductors in a slotis more consistent.

Similar to the embodiment in FIG. 67, this embodiment uses an axial flowchannel at the end of a post to provide a radial/circumferential/axialflow path for fluid to enter or exit the radial flow path channels.

All conductor embodiments that provide coolant flow channels may bepotted with varnish or a potting compound for rigidity and for heattransfer during assembly into the stator. To maintain the coolingchannels after the potting compound or varnish etc has hardened, thestator should be spun to centrifuge the potting compound or varnish etcfrom the large flow channels. Gravity drip draining may work for lowenough viscosity compound or pressurized gas flow through the channelsduring the setting/curing/drying process may also be used to ensure thatflow passages are opened and stay open until the potting compound,varnish etc. sets. The viscosity of the compound and the liquid compoundremoval method and the near-contacting gaps between the conductors andposts should be sized such that the liquid removal process clears thecompound from the channels but allows compound or varnish etc to remainin the near contacting gaps.

Exemplary Flux Control Structures in an Electric Machine

A winding shown in FIG. 79 allows non-straight post shapes such ascurved or variable width posts 2226.

To increase the flux from the permanent magnets across the airgapbetween the rotor and stator the flux linkage path from the N side of apermanent magnet to the S side of a permanent magnet may be reduced. Inan axially aligned permanent magnet rotor, this can be done with a solidback-iron made of a soft magnetic material such as, but not limited to,steel, as shown in FIG. 102. In this case, the flux from a permanentmagnet 2370 will link to an adjacent permanent magnet 2370 through theback-iron 2372 and/or to the opposite polarity face of an opposingpermanent magnet 2370 on the opposite axial face of the backiron 2372.

The torque generated by an Axial Flux Permanent Magnet (AFPM) machine isaffected by, amongst other things, the density of the flux interactingbetween the rotor and the stator. In order to maximize the flux densityat the rotor/stator interface, and thereby maximize the torque that canbe generated, a rotor may use soft magnetic material fitting closelybetween the tangentially orientated pole faces of the permanent magnets(PM's) to channel the flux to the stator interfaces on both ends of therotor. Because the axial dimension of the PM's can be much greater thanthe available tangential space available for them, and the soft magneticmaterial has a higher saturation value than the PM's, the flux densityinteracting with the stator is increased. The PM's are arrangedtangentially NSSNNSSNNS etc. such that two of the same polarity polesare facing each other tangentially. The alternating orientation of thePM's means that the soft magnetic material inward and outward extensionsbetween them become polarized alternately SNSN etc. with each radiallyextending flux path member is the same polarity at both axial ends. Theextent of the axial dimension of the PM's can be changed to suit theirstrength, so that relatively high torques can be generated using lowerstrength magnets. The axial dimensions are such that the PM's neverprotrude beyond the alternating polarity axial faces.

To accommodate relative angular movement and deflection due to externalloading there will normally be an axial gap between the axial faces ofthe rotor and the stators, referred to as the airgap. The flux from thePMs generates alternating poles in the soft magnetic radial membersmaterial between them, and the poles of the electromagnets of the statorprovide a flux path to connect these alternating poles, even with nopower supplied to the EMs. This results in an attraction force betweenthe rotor and the stators. The attraction force between the rotor andstator is higher if the airgap is smaller, so although with an identicalairgap on both ends of the rotor the attraction forces toward thestators would be equal and opposite, any variation in the airgaps at anyangular position will result in a net force that will augment thedisplacement. This tendency requires a bearing and adequate rotorstiffness to avoid contact between a stator and rotor during operation.

The design described below incorporates a one-piece rotor structurewhere a soft magnetic material such as steel or iron or a cobalt orother soft magnetic material or alloy, which is used to carry the flux,also provides structural stiffness. Bearings, such as, but not limitedto a pre-loaded a pair of angular contact bearings, provides momentstiffness between the rotor and the static structure necessary tocontrol deflection and avoid resonances.

In an embodiment, the rotor 2228 as shown in FIG. 80 to FIG. 86 hastangentially polarized permanent magnets 2230 that are arrangedNSSNNSSNNS etc. such that two of the same polarity poles are facing eachother tangentially. The outer region 2234 of the rotor 2228 comprises anarray of inwardly projecting regularly or equally spaced radial fluxpath members 2232 which are interdigitated with an equal number ofregularly or equally spaced outwardly projecting radial flux pathmembers 2236 on the inner region 2238 of the rotor and provide a fluxpath for permanent magnets 2230. Interdigitation of the radial members2232, 2236 helps make the rotor 2228 very rigid. Interdigitationovercomes the challenge of providing a one-piece (or two-piece) ferriticstructure without creating a flux linkage path that would short-circuitthe magnets 2230. The rotor 2228 should be sufficiently rigid thatflexing during operation of the rotor 2228 is a fraction of the airgaplength.

As a result of the tangentially alternating orientation of the permanentmagnets 2230, all of its inwardly projecting radial flux path members2232 which are one piece with the outer region of the rotor 2234, willbe of one polarity, and the outwardly projecting radial flux pathmembers 2236 which are one piece with the inner region 2238 of therotor, will be of the opposite polarity. In this exemplary embodiment,only the inner region 2238 of the rotor 2228 is supported, such as bybearings (not shown), to the stator housing (not shown), althoughadditional bearings may be used. The use of bearings on the ID of therotor, only, can reduce manufacturing cost, and motor/actuator weight,and is made possible by the high strength and stiffness of the rotor. Inan embodiment, the inner and outer regions of the rotor 2228 areintegrally connected by small tabs 2240, 2242 shown in FIG. 82 and FIG.83. FIG. 82 shows that the structural connection between the inwardmembers 2232 and the inner part of the rotor 2238 and the outwardmembers can be through reduced axial width tabs 2240 and/or through thepermanent magnets (not shown). FIG. 83 shows the structural connectionbetween the outermost end of the outward members 2236 and the outer part2234 of the rotor 2228 through reduced axial width tabs 2242. These tabswill create a flux return path from N magnet faces on one of the inneror outer rotor rings 2238, 2234, to S faces of magnets on the other ofthe inner or outer rotor rings 2238, 2234. This flux return path willreduce the airgap flux density in the airgap between the rotor 2228 andthe stator (not shown), but it has been shown by FEA and FEMM analyses,as well as prototype testing, that the connection strength and stiffnessbetween inner and outer rotor members 2238, 2234 is adequately achievedby an array of tabs 2240, 2242 with a small enough cross section toallow only a small percentage of permanent magnet PM flux to be lost.

FIG. 84 shows an exemplary embodiment of the rotor 2228 without themagnets 2230 in order to show the magnet retainers 2244. These are usedto axially position the magnets 2230 and are located at alternating endsof the slots 2248, requiring that half of the magnets 2230 are insertedfrom one side of the rotor 2228 and the other half of the magnets 2230are inserted from the other side of the rotor 2228 during assembly, asshown in FIG. 85. Each half set of magnets 2230 will have theirpolarities in the same tangential orientation which improves stabilityfor assembly. The magnets 2230 can be secured in position using anadhesive and can be further secured by peening of the open slot ends,such as at two positions of similar radial positions to the retainingtabs 2244 to reduce the local slot width to less than the thickness ofthe magnets 2230. Holes 2245 through the rotor 2228 may allow air toflow such that cooling of the stator electromagnets (not shown) on bothsides of the rotor 2228 can be achieved by flowing air or other fluidthrough only one side of the housing structure (not shown). Thecounter-bored holes 2246 through the rotor 2228 are for clamping duringmanufacture. FIG. 86 has the axial surface of the inner rotor ring 2238and of the outwardly projecting flux members 2236 shown in black toillustrate more clearly that the inward and outward extending flux pathmembers 2232, 2236, may be all made of one piece construction, but thatthe inward and outward extending members 2232, 2236 are magneticallyisolated from each other apart from the reduced cross section tabs 2240,2242. The tabs 2240, 2242 may be small enough in cross section comparedto the radially extending flux path members 2232, 2236 that they will besaturated from the PM flux and will therefore not allow significantadditional flux linkage beyond that flux level.

Other variations include inserts of other, non-magnetic material for thetabs, inner and outer members with radially extending flux path membersas shown here with no connection tabs. In this case the body with themagnets will be the main structural connection between the inner andouter rotor rings.

The magnetic forces generated by rare earth magnets, for example,combined with the flux focusing effect of the flux path members canproduce immense axial forces. In the example shown here at an outerdiameter of approximately 9″ can generate an axial attraction force tothe stator of as high as 1500 lbs. A suitably strong and rigid structuremay be used to prevent damage and problematic vibration during use. Arotor with interdigitating members provides both structural rigidity andflux focusing functions into the same radially extending members. Theinterdigitation of these inward and outward members provides a highsurface area contact between the member tangential surfaces and themagnets for effective flux usage and high strength and stiffness.

Exemplary Rotor for an Axial Flux Electric Machine

The rotor can be made of single piece construction as shown here, or intwo or more pieces that sandwich together. Magnets can be of any shapeincluding tapered in any direction for flux path effects and structuraleffects. Any type of magnets can be used. Any number of magnets can beused. Any width of magnets can be used. One or both axial faces of therotor can be used in combination with a stator. Multiple rotors can beused. Multiple circular arrays of magnets can be used with differentnumbers of magnets in two or more arrays. This rotor can be used withactuators or motors or any magnetic machine or device with any number ofphases or poles.

The design described below incorporates a two-piece rotor structurewhere a soft magnetic material such as steel or iron or a cobalt orother soft magnetic material or alloy, which is used to carry the flux,also provides structural stiffness to position the rotor againstmagnetic forces which can be very high with this device, and to supportthe output load on the actuator. Bearings, such as, but not limited to apre-loaded pair of angular contact bearings, provide moment stiffnessbetween the rotor and the static structure necessary to controldeflection and avoid resonances.

FIG. 87 to FIG. 92 show an embodiment of the rotor 2260 which isconstructed in two somewhat mirror image halves 2262 and 2264 which arethen bolted or otherwise fastened or connected together. In thisembodiment, tapered magnets 2266 can be combined with tapered rotormembers 2268, 2269 to provide mechanical security for the magnets 2266,and also to allow a wider tangential magnet section closer to the centerplane of the rotor 2260 where the flux density of the flux path members2268, 2269 is lower. This makes better use of the space available forthe permanent magnets 2266 and for the space available for the softmagnetic material. FIG. 90 shows the permanent magnets 2266 in the samerelative positions as when they are installed in the rotor 2260. Thisshows how the permanent magnets 2266 are arranged with alternatingtangential polarity, NSSNNSSNNS etc, such that two of the same polaritypoles are facing each other tangentially.

Both halves of the rotor 2262, 2264 comprise inwardly projecting andoutwardly projecting radial flux path members 2268, 2269, analogously tothe embodiment of the rotor 2228 discussed previously. In the exemplaryembodiment 2260 shown in FIG. 87, only the inner region 2272 of therotor 2260 is supported, such as by bearings (not shown), to the statorhousing (not shown), although additional bearings may be used, forexample on the ID or OD of the rotor. The use of bearings on the ID ofthe rotor only can reduce manufacturing cost, and motor/actuator weight,and is made possible by the high strength and stiffness of the rotorwhich makes additional bearings unnecessary for many applications.

In an embodiment, the inner and outer regions of the rotor 2260 areintegrally connected by small tabs analogous to tabs 2240 and 2242 inFIG. 86.

FIG. 91 is a section taken tangentially through both rotor halves 2262,2264 showing the axial extent of the connecting tabs 2270 between theoutwardly projecting radial flux members 2269 and the outer part of therotor 2274. These tabs 2270 will create a flux return path from magnetfaces on inwardly projecting radial flux path members 2268 to theopposite pole outwardly projecting radial flux path members 2269. Thisflux return path will reduce the flux density in the airgap between therotor 2260 and the stator (not shown), but it has been shown by FEA andFEMM analyses, as well as prototype testing, that the connectionstrength and stiffness between inner and outer rotor members 2272, 2274is adequately achieved by an array of tabs 2270 with a small enoughcross section to allow only a small percentage of permanent magnet fluxto be lost. The magnets 2266 are positively retained by their taperedgeometry and can be further secured in position using an adhesive. Holes2275 through the rotor 2260 may allow air to flow such that cooling ofthe stator electromagnets (not shown) on both sides of the rotor 2260can be achieved by flowing air or other fluid through only one side ofthe housing structure (not shown). The counter-bored holes 2276 throughthe rotor 2260 are for clamping during manufacture.

The inward and outward extending flux path members 2268, 2269 may be allmade of one piece construction, but that the inward and outwardextending members 2268, 2269 are magnetically isolated from each otherapart from the reduced cross section tabs 2270 and analogous tabs on theinner part of rotor 2260; these tabs may be small enough cross sectioncompared to the radially extending flux path members 2268, 2269 thatthey will be saturated from the PM flux and will therefore not allowsignificant additional flux linkage beyond that flux level.

Although, as described elsewhere, bolts, rivets, or similar may be usedto hold the two halves 2262, 2264 of the rotor 2260 together, anadditional or alternative retention method is to use an external ring2278 with one or two internal tapered faces 2280 as shown in FIG. 92.The inside diameter of the external ring can be used to ensureconcentricity between the two halves 2262, 2264 of the rotor. Thisexternal ring 2278 could be installed by generating a thermaldifferential between it and the two halves 2262, 2264 of the rotor. Theuse of a high expansion material for the ring 2278 such as, but notlimited to, an aluminum alloy, would reduce the temperature differencenecessary to install the ring 2278.

Various embodiments may include: one rotor adjacent to one stator, arotor is on each side of one stator, a rotor is on each side of a pairof back-to-back stators, or combinations of these configurations.

Exemplary Axial Flux Electric Machine with Two Piece Stator BetweenRotors

FIG. 93 to FIG. 97 show an electric machine 2281 in which a rotor islocated on each side of a pair of back-to-back stators FIG. 94 showsthat the rotor 2282 comprises two somewhat mirrored halves 2283supported from the stator baseplate 2284 by, in this example, twoangular contact bearings 2286. As with the previously described designshaving the rotor between the stators, the outer region of each half 2283of the rotor comprises an array of inwardly projecting equally spacedradial flux path members 2288 which are interdigitated with an equalnumber of equally spaced outwardly projecting radial flux path members2290 on the two halves 2283 of the inner region of the rotor 2282, asshown in the expanded view of the present embodiment in FIG. 93. Thestator baseplate 2284 may be of a high thermal conductivity materialsuch as aluminum. The construction of a stator 2292 of this embodimentis shown in FIG. 95. The stator 2292 comprises a backiron 2294, posts2296, and axial protrusions 2298 from the back of the backiron. Theaxial protrusions 2298 on the back surface of the stators are secured inslots 2300 on the stator baseplate 2284 by mechanical means or anadhesive bond, as shown in FIG. 96. A cross section of the device 2281is shown in FIG. 97. Radial channels 2302 are formed between the statorposts 2296, the stator back iron 2294, and the stator baseplate 2284 forthe flow of fluid such as air or liquid or a phase change fluid that maybe used to cool the device 2281. Each stator post 2296 is supportedthrough the thickness of the back iron 2294 and engages in a slot 2300in the stator baseplate 2284. The stator assembly used here shows thestator posts 2296 fused to the back iron 2294, so no interface lines aretherefore visible. Tapered magnets 2304 are used in this example as theattraction force towards the stator 2292 secures them into the body ofthe rotor 2282. The conductors that are positioned around the statorposts are not shown in these figures, but would be similar to thosedescribed in configurations with the stators located outside of therotor.

Exemplary Axial Flux Electric Machine with Stator Between Rotors

Another embodiment comprises one rotor on each side of a one-piecestator. FIG. 98 show a cross-section of such an embodiment of electricmachine 2306. The rotor comprises two somewhat mirrored halves 2308supported from the stator 2310 by, in this example, two angular contactbearings 2312. As with the previously described designs having thestator between the rotors, the outer part of each half 2308 of the rotoris analogous to the rotor in FIG. 81, comprising an array of inwardlyprojecting equally spaced radial flux path members which areinterdigitated with an equal number of equally spaced outwardlyprojecting radial flux path members on the inner part of the rotor. Toprevent flux flow between the two halves 2308 of the rotor they bothhave the same polarity. Because the inner part of each rotor half 2308becomes polarized according to the orientation of the poles of itsmagnets, the same magnet pole is to be placed against the outwardlyprojecting radial flux path members on each rotor half Holes 2314 areshown through the center part of the stator 2310 that can be used tocarry any fluid that may be used to cool the device 2306. A crosssection of the device 2306 is shown in FIG. 99. Tapered magnets 2316 areused in this example as the attraction force towards the stator 2310secures them into the body of each rotor half 2308. The stator 2310comprises two somewhat mirrored sets of stator posts 2318. Theconductors that are positioned around the stator posts 2318 are notshown in these figures, but would be similar to those described inconfigurations with the stators located outside of the rotor.

Conductive heat transfer of this embodiment is similar to the otherembodiments with regard to the low heat flow resistance from theconductors to the heat dissipation surface, except that in this case,the top of the conductors at the airgap is a heat dissipation surface.For cooling, active circulation of a cooling fluid through the airgapmay be provided. Direct cooling of the coils will also benefit from thisgeometry in this configuration compared to geometry outside of thedisclosed range. A similar configuration could be done with one statorand one rotor.

Exemplary Robotic Structure

The following is given as a non-limiting example of how an actuator(motor having one of the disclosed configurations of slot density andconductor volume, or other disclosed features) may be used in a roboticapplication. A schematic of this example system is shown in FIG. 100. Anexample system consists of a static robotic arm 2336 supporting anominal payload 2338 of 10 kg, and having four actuators 2340, 2342spaced along the arm. Thus, at least one actuator 2340, 2342 on therobotic arm 2336 is supported by another actuator. Three of theactuators 2340 may be identical in size and torque-production capabilitywith two being located at the shoulder joint and one at the elbow joint.The remaining actuator 2342, located at the wrist, is half the size andweight of the previous actuators. The wrist actuator 2342 is inactive inthis example and will be considered only for the weight that it adds tothe system. The active actuators have an average airgap diameter of 200mm and a radial tooth length of 32 mm. The housing and peripheralsassociated with each actuator 2340, 2342 are estimated to equal theactive weight of the actuator, such that the total weight is estimatedat twice the active weight. The distance between actuators 2340 fromcenter to center is 0.5 m. The weight of each arm 2336 is estimated at20% of the total mass of any downstream system components including thenominal payload 2338. The simulation in this example applies a forcedliquid cooling rate of 700 W/m²K to the back of each stator in eachactuator 2340. The system is analyzed in a stationary position where thearm 2336 is horizontal and supplying sufficient torque to hold thepayload 2338. The power consumption of the system is equal to the totalpower consumed by the elbow and two shoulder actuators 2340. In thisexample, it is found that the system power consumption dropssignificantly inside the disclosed range. This is due to the compoundingeffect of the weight of the device on the required torque. As the weightof each individual actuator drops, the torque required from any upstreamactuators is reduced. For any particular system with a specifiedstructure and payload, there exists ageometry where the system powerconsumption is minimized. The calculation required to come to thisconclusion assumed a 70° C. temperature limit for continuous torque. Anygeometries in which one actuator in the system must surpass thistemperature limit in order to support the payload are classified asoverheating and excluded. Geometries with very large slot pitch andconductor volume overheat because upstream actuators are not able toproduce sufficient continuous torque to support downstream actuators.They are limited by the actuator weight. Geometries with very small slotpitch and conductor volume overheat because upstream actuators are notable to produce sufficient continuous torque to support the payload.They are limited by the payload weight. The optimum geometry for anyparticular system will be a balance between generating sufficient torqueto satisfy the system requirements and minimizing the actuator weight toreduce the overall power consumption.

FIG. 101 shows a mounting configuration for an electric machine on arobotic arm 2348. The set up may be as schematically illustrated in FIG.101, with three or more actuators. Electric machines 2350 and 2352 maybe designed as disclosed with any one or more of the novel featuresdisclosed, for example as shown in FIG. 56. The electric machines 2350and 2352 operate as actuators in this example and will be referred to assuch. Actuator 2350 is supported by a first housing or structural part2354 of the robotic arm 2348 by any suitable means. Electric power maybe provided to actuator 2350 by a cable 2356 from a suitable powersource (not shown). The housing part 2354 may attach to a supportingstructure, for example another part of a robot or a wall 2355(illustrated schematically).

A second housing part 2358 is secured to rotor 2360 of actuator 2350.Actuator 2352 is secured to housing part 2358 by any suitable means sothat actuator 2352 is supported by actuator 2350. Power may be suppliedto actuator 2352 by cable 2362. Rotor 2364 of actuator 2352 is securedto a third housing part 2366 of robotic arm 2348 by any suitable means.A further actuator, illustrated in FIG. 100, may be incorporated in thehousing part 2366, and this actuator may be made in accordance with FIG.56 and supplied with power from cable 2368. The actuators 2350, 2352 andother actuators on the arm may be made smaller with increasing distancefrom support 2355. Any of the actuators on the robotic arm 2348 may besufficiently spaced along the arm to have 360-degree rotation, forexample actuator 2352.

Solid and Laminated Stator or Rotor Constructions

In some embodiments, a laminated stator or rotor may be used. In FIG.103 a laminated post stator configuration is shown. This exemplaryembodiment has an array of slots 2380 to receive the array of laminatedposts 2382. The backiron disk 2384 can be a laminated construction or asintered construction or a solid construction as shown here. The linesof flux travel generally tangentially in an axial flux motor so aneffective laminate structure will need to have the laminates for eachpost and backiron aligned tangentially. One method of achieving thisalignment is to coil a strip of laminate in a tight spiral, like a rollof tape, with an adhesive layer between each laminate layer. After thecoil is cured, material is removed by a machining process to form radialposts and slots.

The high number of relatively small posts of an embodiment of anelectric machine with features in the disclosed range makes it desirableto use as few parts as possible in the construction of the stator. Iflaminates are used, the number of laminated parts can be reduced by theuse of radially aligned laminates as shown in FIG. 104. A drawback ofthis embodiment construction is shown schematically in FIG. 104 at thejunction of the backiron 2384 and a laminated post 2382 where the flux2386 that links from post to post though the backiron 2384 must passthrough one or more insulation layers 2388 between the lamination layers2390. The insulation layers (shown schematically at post 2382 as heavylines) are useful and possibly necessary for the reduction of eddycurrents, but they act as airgaps which increase the reluctance of theflux path with a resulting loss of torque and efficiency. Anotherdrawback of this construction geometry is the minimal glue line 2392that results from the very thin backiron 2384 of an electric machinehaving features in the disclosed range. Considering the very high axialloading on the posts 2382 of an embodiment of an electric machine, itmay be structurally unsound to rely on this glue line 2392 for someapplications.

A construction is proposed to help prevent stator posts from beingpulled out of their slots while at the same time providing metal tometal contact between the posts and backiron so the flux is not forcedto cross through any insulation layers. FIG. 105 and FIG. 106 show anon-limiting exemplary embodiment of a laminated post construction of astator 2398 and housing or cover member 2412 that provides adequatepull-out strength as well as metal-to-metal contact for the majority ofthe flux linkage connection between the back iron 2400 and the posts2402. To accomplish the necessary structural integrity, the posts 2402extend through the backiron 2400 enough to provide multiple functions.The extended material allows the use of a tapered barb 2404 to allowease of assembly and provide a mechanical pull-out stop. In thisnon-limiting exemplary embodiment, a barb 2404 is proximal to a slit2406 which is long enough to allow elastic deformation of a post 2402during assembly. Other mechanical means may be used to act as mechanicalpull-out stops, allowing insertion of the posts from one side andsubsequently providing resistance to extraction of the posts from thatside. For instance, a ratchet-like design may be used, with contactingsurfaces of the posts and the backiron shaped in a manner that preventsthem from sliding past each other in the direction of extraction underthe application of pressure to the surfaces, either by a springconfigured to do so, or by other mechanical means, activated afterinsertion of the posts into the stator.

The protruding section 2408 of a post 2402 beyond the back surface ofthe backiron 2400 is inserted into a slot 2410 of similar width in thecover member 2412. In an embodiment, this cover 2412 is made of alightweight material such as aluminum or a composite such as carbonfiber. The surface area of the protruding section 2408 of a post 2402 isadequate to allow the bond with the cover slots 2410 to add thenecessary rigidity to the assembly to withstand the high magnetic forcesof an embodiment of an electric machine having features in the disclosedrange. The embodiment shown comprises one central laminate 2409, with aprotruding section 2408, per post; however, more than one laminate witha protruding section can be used per post.

Radial spaces 2414 between the slots 2410 on the inner surface of thecover member 2412 can be used for weight reduction and for flow ofcooling fluid. Also shown in FIG. 106 is the use of a slit 2416 in thepost 2402, passing through the protruding centre laminate 2409 as wellas through the axially shorter laminates 2418 on a post 2402, eventhough the shorter laminates 2418 do not comprise a barb 2404. This isto allow the barb 2404 on the protruding laminate(s) to flex duringassembly.

Each post 2402 in this exemplary embodiment is glued together insub-assemblies before insertion into stator slots 2420. Conductors (notshown) are then wound or placed around the posts 2402 and conductors arethen potted with a potting compound. In addition to the stabilizingeffect of the cover member slots 2410, the potting compound will serveto provide circumferential strength and rigidity to the laminated posts2402.

Note that powdered metal or solid material can be used with similarretaining features as shown here for the laminated posts. If solid orpowdered metal is used for the posts, it is believed to be less complexand expensive as well as mechanically stronger to make the posts andbackiron of unitary construction.

Magnetic flux path integrity is achieved in this exemplary embodiment bythe use of axially shorter laminates 2418 on the side of a longerlaminate 2409, of which a part 2408 protrudes through the backiron 2400,as demonstrated in FIG. 107. To achieve adequate metal-to-metal contactbetween the stator backiron 2400 and posts 2402 for low reluctance fluxlinkage 2424, all insulation at the junctions 2426 between the backiron2400 and the laminates 2409 and the junctions 2428 between the backiron2400 and the laminates 2418 have been removed, as shown in FIG. 107. Theremaining insulation 2430 is shown schematically at one of the posts2402 as a heavy line. Unlike the removal of insulation from the fluxpath of the exemplary embodiments in FIG. 104 at 2388, the removal ofinsulation in FIG. 107 at 2426 and 2428 results in metal-to-metalcontact both between laminates 2409 and the backiron 2400 and betweenlaminates 2418 and the backiron 2400 for low reluctance flux linkage2424.

In the exemplary embodiment shown in FIG. 107, the use of a solid backiron disk 2400 is believed to reduce eddy currents substantiallycompared to a 100% solid stator and posts due to the backiron being arelatively small part of the flux path (not shown) and because thebackiron disk 2400 can be axially thick enough to reduce the fluxdensity compared to the flux density in the posts 2402. Eddy current andhysteresis losses increase with flux density, so for certainapplications where the benefit of laminated posts is deemed to beworthwhile, the use of a backiron disk made of a solid metal such asiron or a cobalt or nickel alloy may offer adequate efficiency and thenecessary structural integrity. With solid material used for thebackiron an alloy with low electrical conductivity (and high heatconductivity) and high flux density may be used.

Adhering the protruding post sections to the slots of the cover can bedone with epoxy or other adhesives or solder or brazing or ultrasonicwelding, etc. A high strength solder has the advantage of providing goodheat transfer which is helpful for cooling.

Aluminum Conductor Coating Construction and Method

Some embodiments of the electric machines disclosed comprise coatedaluminum conductors. A process of manufacturing and coating of aluminumconductors for electrical machines is disclosed which includes creatingan anodized surface finish on the conductors for electrical insulationin such a way that high heat dissipation and low cost manufacturing ofthe conductors is possible. The procedures described may also utilizevarious construction and assembly steps to achieve high current density,especially when used in combination with motor/actuators in thedisclosed range. This process may be used in the manufacture ofelectrical machines such as, but not limited to, an embodiment of anelectric machine.

It is beneficial to embodiment of the disclosed electric machines, andto electrical machines in general, to create a conductor constructionthat has light weight, good heat transfer and low cost. Electric motorconductors are commonly made from copper wire that is pre-insulated witha polymer coating or aluminum wire or foil. Advantages of aluminuminclude much lower weight per volume and lower cost as compared tocopper. A downside of aluminum is that it has higher electricalresistance than copper and produces more heat for the same currentdensity. One method of pre-insulating aluminum conductors is to use ananodized surface finish. Advantages of anodizing are a very hard surfacethat protects the wires during assembly, high dielectric strength, and 2to 4 times better thermal conductivity as compared to an exemplarypolymer film as used on common wire conductors.

Anodized aluminum conductors provide the potential for low cost, highsurface strength and light weight, but they are typically limited inseveral respects.

One problem relates to sharp edges. As shown in FIG. 108, anodizing,such as oxalic or suphiric acid anodizing, “grows” a layer of aluminumoxide 3110 outward and inward perpendicular to the original aluminumsurface. This leaves a less or non-insulated area at any sharp edge,referred to as a corner gap 3108; corner gaps may also be referred to asedge gaps. As a result, anodized aluminum conductors require roundededges to prevent these un-insulated sections from forming. Roundingthese edges is expensive because it requires additional mechanical orchemical processing. A radius of 0.015″ is known to be required for goodedge coverage with hard anodizing, so a minimum conductor thickness of0.030″ is required. This is a very thick conductor and would requireunacceptably high current due to the low number of turns in a slot inmany applications.

When flat, conical, etc. conductors 3100 are formed, such as with alaser, die, knife, punching or fine blanking process, rounding theseedges, such as with a chemical or mechanical process, will also resultin reduced conductor cross section area. This results in higher currentdensity and higher heat production for a given current, as well as theloss of surface area between conductor layers to transmit this heat tothe top or bottom of a slot. The combination of these three effects isenough to produce significantly higher temperatures in an electricalmachine as compared to the use of sharp cornered conductors of the samethickness and width.

These principles are also true of a polymer coating insulator on copperor aluminum (or other conducive material) conductors but for differentreasons. The surface tension of polymer coating systems tends to pullthe coating away from sharp edges, for this reason, it will produce amore even coating if the edges of a wire or conductor are rounded.

A comparison of the schematic stator sections of two exemplaryembodiments is shown in FIG. 109 and FIG. 110. One stator comprisesconductors with sharp edges and the other stator comprises conductorswith rounded edges. Both stators are within the disclosed range, but theprinciples will apply to stators outside of the disclosed range with apercentage of the benefit. The conductors are 0.100″ wide with athickness of 0.020″. The stator in FIG. 109 comprises copper conductors3130 with a thermal conductivity of 390 W/(m*K), rounded edges and apolymer coating 3134 with a heat thermal conductivity of 0.17 W/(m*K),whereas the embodiment shown in FIG. 110 comprises aluminum conductors3110 with a thermal conductivity of 220 W/(m*K), sharp edges, and a hardanodized coating of 0.001″ thickness and a thermal conductivity of 0.75W/(m*K). For the same thickness and width, the square conductor has ˜5%greater cross sectional area, ˜20% higher heat transfer contact areawith adjacent layers and nearly twice the potential heat transfercontact area with the posts. Due to the i² loss associated with currentdensity, the 5% loss of cross section in the rounded conductors resultsin a reduction of the permissible current density of approximately 10%,while the reduction of heat transfer surface area between the roundedconductors of 20% to 30% results in a reduction of the current densityfor a given stator temperature of up to 30% or more, this is asubstantial reduction of the possible motor performance. For thesereasons, combined with the cost benefit of being able to form aluminumconductors with a high speed process, such as fine blanking, and thenanodize them without rounding the edges, this conductor method andconstruction offers significant cost and performance benefits. It hasbeen shown, by FEA analysis, that the conductor configuration disclosedhas significant enough benefits that when the use of square/sharp edgedaluminum conductors is combined with a high heat transfer electricalinsulator such as anodizing, the higher electrical resistance ofaluminum, as compared to copper, can be partially or more than offset,in some cases, by the increased cross-sectional area of the aluminum andthe increased heat conduction of the anodized layer as compared topolymer insulation coating on copper conductors.

Based on an FEA heat transfer analysis, it has been found that theeffect of the higher conductivity and heat transfer surface area of thealuminum conductors is, in this example, adequate to maintain a similarmaximum conductor temperature as copper conductor example, even thoughthe aluminum conductors are higher resistance and are producingapproximately 50% more heat. There is thus a benefit of anodizedaluminum conductors compared to polymer coated copper conductors with asimilar maximum conductor temperature. The aluminum conductors requiremore power, but they are ⅓rd of the weight of the copper conductors sothis increased power is offset to a certain degree by the reduction ofthe actuator mass and increased KR. The challenge with anodized aluminumconductors is that is to achieve good edge coverage with an edge radiusof 0.010″ or less for many processes. This requires that conductors bethicker than 0.020″ and preferably a minimum of 0.030″. This is notpreferred for many motor applications where thinner conductors willreduce the required current by allowing more turns. This results in thesituation where conductors of 0.020″ or less will benefit from a surfacefinish coating system that protects the sharp edges.

In an embodiment of, an electric machine may take advantage of low costmanufacturing processes which leave a sharp edge to provide increasedcross sectional area while providing methods of protecting theun-anodized sharp edges. In an embodiment, the edge protecting systemalso serves to provide a method of securing the conductors in the slot.The embodiment also uses the sharp edge insulating method to secure theconductors in the slot and to provide a high percentage of conductorsurface area exposed to a cooling fluid.

A non-limiting example of the process of insulating the sharp-edgedaluminum conductors is as follows. The aluminum conductors 3100 may bepunched or stamped or fine blanked or laser cut, etc. from sheets ofaluminum in a specified pattern intended for stacking between statorposts. The aluminum conductors should be made by a method that leaves areasonably square edge. This prevents the anodized surface from formingoutward form the sharp edges so the surface tension will be prone tohold a liquid dielectric material, or the increased static charge at theedges will tend to attract a dielectric powder coating material. Manytypes of aluminum can be used. 1100 series aluminum is known to havehigh electrical and heat conductivity which is beneficial for thisapplication. Two adjacent layers 3102 of stackable flat conductors areshown side by side before assembly in FIG. 111. The conductors shown inthis figure are designed to be stacked in alternating order. Eachconductor layer E3102 serves as a conducting path for the flow of acurrent. Each conductor layer includes a pair of contact tabs E3106which may be connected into a circuit to allow the flow of a currentthrough the conductor. Many different flat and non-flat aluminumconductor configurations can be used in combination with aspects of theconductor insulating system disclosed here.

The conductors may then be masked at the contact tabs 3106 to reducepreparation time after anodizing and before connecting layers 3102together. The parts are then hard anodized on the remainder of thesurfaces. The anodizing process ensures coating and protection of thetop, bottom and side surfaces. Due to the anodized layer 3110 growingperpendicular to the original aluminum surfaces, any orthogonal surfacesof the anodic coating will form corner gaps 3108 between them (FIG.108).

When coating a sharp edge with a polymer, it is expected that surfacetension will cause a thinning of the coating at the sharp edge.Similarly, but for a different reason, an anodic process applied toaluminum will create an unprotected area at all sharp edges due to theperpendicular growth of the coating. But while both of these coatingmethods are inadequate on their own, the sequential combination of ananodic coating 3110 followed by a dielectric polymer coating 3112creates a favorable condition where the gap 3108 produced by theanodizing process results in a surface tension effect that draws theliquid polymer into the gap 3108 in the anodic coating 3110.

The polymer coating 3112 can be applied by dipping or spraying theconductors. Many different polymer or other liquid coatings such asvarnish can be used. If an epoxy coating is used, it can be cured orbaked to a B state and then a final cure phase can be applied afterfinal assembly of all conductors into the stator. During all coating andcuring processes, it is believed possible with adequate process control,to maintain a favorable condition so the meniscus formed between theperpendicular surfaces of the anodic coating will maintain a thickenough polymer coating for many applications. FIG. 112 shows an exampleof a coated conductor, with dielectric coating over the surface of ananodized conductor. The thin coating on all surfaces is not necessary inmany applications for insulation as the anodic coating is very effectiveon flat surfaces. With a low viscosity polymer it is believed possibleto ensure the flow of polymer into the edge gaps while at the same timeproviding a thin layer of coating on the rest of the conductor that canbe used during final assembly to fix the conductors in the stator byheating or another final adhering process condition. FIG. 113 shows theexpected result of a concave meniscus forming by dielectric coating andcoating the corners. When curing or baking the conductor layers theconductors layers may be cured or baked together in a stack to create aunified structure.

In an embodiment of the disclosed electric machine in an assembledstate, the masked tabs 3106 are soldered or welded together afterconductors 3100 are stacked together into layers as shown in FIG. 114with the conductor pair stacked between stator posts 3114 of the stator3116. Note that these areas can be spot welded, laser welded, or plugwelded or joined by mechanical means during or after assembly of alllayers. The final step may include, for example, baking the assembledcomponents in order to fuse and cure the dielectric coating as well asadhering the conductors together and to the stator.

This coating system has a number of useful features and benefits. Onebenefit is the potential for high-speed fabrication of conductor parts,for instance by fine blanking, which method has the advantages of lowcosts and inherently high precision. There is minimal or no need forfinishing edges, which reduces costs and allows greater surface area(with aluminum) to help offset higher resistance of aluminum as comparedto copper (which must have rounded edges to achieve even coating). Adeburring process may be helpful, but requires minimal processing.

The disclosed coating system allows for the practical use of aluminumconductors, which have a lower cost than copper and a third of theweight. The coating system results in a very hard anodic coating, whichis harder than polymer coating, allowing a tighter fit with the statorwithout damage. A hard anodic coating also typically has higher thermalconductivity than polymer coating, sometimes by a factor of three orfour. The coating system allows aluminum conductors to be much thinnerthan the known 0.020-0.03 minimum thickness to allow a 0.010″-0.015″radius on all edges. Thinner conductors allow lower current by providinga higher number of turns. In some embodiments of the disclosed machine,thinner layers also provide greater surface area per slot for directcooling of conductors.

The coating system works especially well with embodiments of thedisclosed machine when used with conductor layers having the same phase.In an embodiment, there is minimal voltage potential between layers dueto all layers in a section being of the same phase. This allows thinneranodic and polymer edge coating. The absence of interweaving ofconductors from different phases allows layered construction. Minimalelastic and minimal or no plastic deformation of conductors allows thebrittle anodic coating to remain intact during assembly.

Another non-limiting example of a process of insulating the sharp-edgedaluminum conductors involves powder coating. Powder coating is typicallyused to apply an even coat of polymer powder to a part with the oppositestatic electric charge of the powder. The powder is then fused to thepart as a continuous coating by the application of energy, usually inthe form of heat, such as by baking the conductor layer. Conductorlayers may be backed in a stack to produce a unified structure. Analuminum conductor with sharp edges can be sprayed with an oppositecharged dielectric powder or dipped in a fluidized bed of oppositelycharged dielectric powder. The anodizing layer is believed to provide aninsulator to reduce the static charge from causing adequate attractionbetween the powder and the flat top and bottom and edge surfaces, whilethe less insulated gaps at the sharp edges are expected to result in abiasing of the attraction of the powder to the conductor edges. Theconductor is then removed from the spray or fluidized bed and semi- orfully fused to the conductor and semi- or fully hardened. If an epoxydielectric powder is used, the powder may be partially cured after theedges are coated. The conductors and then assembled into the stator (oraround a core, or into some other aspect of an electrical machine).After final assembly the edge-coating is then fully cured and in theprocess bound to the stator and other conductors.

Depending on the process conditions it is expected that the powdercoating of the edge can provide partial or complete or more thancomplete coverage of the edge gap in the anodic coating. FIG. 115 showsan exemplary embodiment with complete coverage of the gaps at the sharpedges. FIG. 116 shows an exemplary embodiment with more than completecoverage. Another exemplary embodiment may comprise the embodiment shownin FIG. 115 or FIG. 116 with a second polymer coating 3120 such as athermoplastic or epoxy or varnish, as shown in FIG. 117, applied to theconductor layer to provide an adhesive layer for allowing the conductorsto be adhered together in the final assembly.

Whether an additional adherent 3120 is used or if the edge powdercoating is used as the adherent, embodiments can be assembled with athin layer of a removable material such as, but not limited to PEEK orUHMW between the conductors. The parts may then be cured, for instancewith heat, and then the spacer layers are removed by pulling them out.

FIG. 118 shows a section view of an assembled stator 3116 and conductors3100 with a spacer 3118 between one or more conductor layers 3102 in oneor more slots. FIG. 119 shows a section view of the conductors andspacers before spacer removal with the powder edge coating contactingand adhering the conductors to each and/or to the post sidewalls. Havingthese minimal adhesion points reduces the conductive heat dissipationfrom the conductors to the stator, but it allows greater surface area tobe exposed to a cooling fluid such as air or liquid or a multi-phasefluid that can be used to draw heat away from the conductors.

A material like PEEK or UHMW will stretch to a second material conditionwhere the molecules are more aligned and the plastic retains a highpercentage of its strength, but it becomes significantly thinner so asto allow removal from between the conductor layers when used as aspacer. PEEK has been found to be very strong when stretched and is alsovery heat resistant to allow it to withstand a typical heat curingprocess, but PEEK must be used with a mold release coating or withadhesives which do not adhere to it. UHMW is less strong but hasexcellent release properties which allow for removal without releaseagents.

A simplified section of a stator 3116 with a spacer 3118 component beingremoved is shown in FIG. 120, with the thinning of a section of thespacer as a result of stretching the material. A material such as PEEKwith a thickness of 0.004″, for example, will stretch to a newplastically deformed mode where the thickness is only 0.003″. Thisprovides 0.001″ of clearance for the removal of the spacer. Thestretching and consequently thinning of the spacer happens as a resultof the friction or bond with the conductors along the length of thespacer and the tension applied to the externally located end of thespacer. As the spacer stretches and thins, the leading edge of thefriction or adhesion contact surface travels in the opposite directionof the external end which is being tensioned until enough of the spaceris stretched/thinned to allow complete removal of the spacer.

Instead of a polymer or other adhesive, if a high enough temperaturepowder coat is used, a metallic solder is believed possible to be usedto adhere the conductors together and to the stator. This has theadvantage of very high heat transfer as compared to a polymer.

Anodized conductors of the described construction can be used on avariety of electric machines, including, but not limited to, axial fluxmachines, radial flux machines and linear actuators.

Exemplary Electric Machine with Non-Planar Rotor and Stator

Some embodiments of an electric machine comprise a rotor comprising anannular disk, with holes extending through the plane of the disk. Insome embodiments, the holes extend between the inner edge and the outeredge; in other embodiments, holes may extend only partway through thedisk. Holes that are circular in cross section, with the plane of crosssection being orthogonal to the plane of the disk, may provide the rotorwith roman arch support, conferring rigidity to the rotor. The use ofholes in the rotor decreases the amount of material in the rotor,resulting in a lower mass. The holes may extend radially, though notperfectly radially; however, other arrangements are also possible, suchas a spiral arrangement. The holes may be parallel to the slots; theholes may align with the slots on a projection onto the axial plane. Theholes and slots may be connected by openings. The rotor may bemanufactured of a unitary piece of a material such as steel or iron, andthe rotor posts may be formed of the unitary piece. Posts may extendbetween the inner edge and the outer edge of the rotor. The rotor postsmay define straight lines between the inner edge and the outer edge, andmay be substantially parallel to each other. Such a configuration canfacilitate magnet insertion. Posts may have an inverse taper (narrowing)of circumferential thickness with axial height, for improved magnetretention. On a double-sided rotor, there may be posts on each side ofthe rotor, and posts on one side of the disk may be aligned withrespective posts on the opposite side of the disk as projected onto aplane perpendicular to the axis. The rotor may be stiffened with lowdensity magnesium or aluminum rings. The axial cross-section of therotor may have different thickness at different radial distance from thecentre. In particular, the rotor may have a smaller axial height at aradial distance from the centre of the rotor greater than the innerradius and smaller than the outer radius.

Embodiments described above, comprising a rotor with holes, have anumber of advantages. The mass of the rotor is decreased, as itcomprises less material. The small cross section of the rotor in thetangential direction aligned with the flux path, compared to the crosssection of the magnets, results in low flux leakage and high possibleflux density, further increased by the use of tapered magnets. Romanarch support confers rigidity. The absence of extended thin sectionsresults in shear load rather than bending load in all stressed areas.There are no thin sections of appreciable length to cause flex. Sincethe stress is comparatively low, low cost materials, such as Durabar™may be used to attain sufficient stiffness. The rotor may be constructedwith only an inner bearing, which is advantageous in terms of cost andmanufacturing complexity, and allows force sensing. An integratedencoder may be used. The possibility of magnet insertion after assemblyof the rotor is also beneficial, as the forces between permanent magnetsmay normally make assembly difficult with permanent magnets presentduring the process. A tapered interface allows full contact of thepermanent magnets with the rotor material, allowing for lowermanufacturing tolerances, and resulting in a slight increase in torque.Tapered slots may be manufactured using a large disk cutter instead of asmall endmill with enough shank at an angle to provide shaft clearance.

Some embodiments of an electric machine comprise a rotor exhibiting oneaxial height or thickness at the inner edge and a second axial height orthickness different from the first axial height at the second edge, anda stator of complementary shape. For example, the second axial heightmay be greater than the first axial height. An exemplary embodimentcomprises a conical rotor and stator. A conical rotor or stator is foundto possess a much higher stiffness than an analogous planar rotor orstator, respectively. High stiffness allows a very consistent and smallairgap to be maintained.

FIG. 123 shows a cross-section of an exemplary embodiment of a conicalrotor 3200, stiffened with low density magnesium or aluminum rings 3212,3214 on the inside and outside of the rotor; the rotor may bemanufactured of steel or iron Conical rotor can be instead anynon-planar surface of revolution, for example having a hyperbolic orparabolic shape. The rotor has an axis, and may have circumferentiallyspaced carrier posts extending axially from the each side of the annulardisk. In such a conical device, the rotor has a variable axialthickness, and on the inside, nearer to the axis, is thinner in theaxial direction than on the outside, although this difference may bereversed so that the rotor is thinner in the axial direction on theoutside.

FIG. 124 gives a close-up cross-sectional view of the embodiment in FIG.123 with the magnesium or aluminum rings removed Even without themagnesium rings, the rotor is incredibly stiff, even though the largestcross section is only 0.015″ thick. The stator slots may be tapered. Thehyperbolic shape of the axial cross section, while not essential, allowsthe construction of a rotor with lower mass, and is well-suited for highspeed machining. Conical or round holes 3222 are drilled through theback-iron 3220 of the rotor, and slots 3224 may be cut with a diskcutter. Both operations are very fast. Such a construction allows themass to be minimized, while providing a roman arch support for all thinsection, and results in a balance of strength and rigidity. Importantly,there are no extended thin sections. Consequently, although there aremany bottlenecks for flux, there are no thin sections of appreciablelength to flex. All stressed areas therefore experience shear stressrather than bending stress. The cross-sectional area between the posts3226 is minimal, yet the stiffness is high.

The output of a computational analysis on 20% of the rotor; with half of500 N of force, shows that the deflection is less than 0.0005″, and themaximum stress is only 2000 psi.

The exemplary embodiment of the rotor shown in FIG. 123 to FIG. 127 hasa number of advantages. The conical shape and roman arches conferconsiderable rigidity, which is important in the maintenance of anecessary minimal airgap. The embodiment exhibits minimal flux leakagedue to the very small cross section compared to magnet cross section (intangential direction aligned with flux path), and highest possible fluxdensity due to the minimal leakage path and the tapered magnets. Theconstruction is light-weight, and can be built with an inner bearingalone. This provides cost benefits and allows force sensing. Anintegrated encoder may be used.

The tapered interface permits full contact of the permanent magnets withthe material of the rotor, allowing for lower manufacturing tolerances.Moreover, the construction allows permanent magnets to be inserted afterassembly of the rotor. Since assembly can be very difficult with thepermanent magnets in place due to immense forces between the magnets,post-assembly insertion is a considerable safety and cost benefit. Themechanical magnetic retention is especially important for configurationsinvolving strong magnetic repulsion between nearby magnets. The minimalleakage path and tapered magnets provide high flux density. Since thestress is low, low cost materials are possible.

Due to the high number of small features, machining could be very timeconsuming, but tapered slots allow: the use of large disk cutter insteadof small endmill with large enough shank at an angle to provide shaftclearance; mechanical retention of PM's; and -5% higher torque. Thegeometry provides ability to achieve the majority of the benefit withlow cost materials such as Durabar™.

Particular Embodiment Having Cooling Fins

The device geometry of the disclosed range will provide torque-to-weightand K_(R) benefits over a range of air gaps between the stator and rotorsuch as, for example, from as low as 0.001″ or lower, and up to 0.010″or higher. The high pole density in the disclosed range results in anunusually short magnetic field which will tend to benefit from smallerair gaps as compared to motors of a given diameter which are outside ofthe disclosed range. It has been shown by analysis and experimentationthat an airgap of 0.005″ for a 175 mm average airgap diameter actuatoris beneficial and achievable with reasonable manufacturing tolerances byimplementing the principles shown here.

FIG. 128 is an axial view of an embodiment of an assembled actuatorincluding power and encoder connectors. As shown in FIG. 128, anactuator 3000 comprises a stator 3002 having fins 3004 and a rotor 3006.The rotor is the assembly shown in FIG. 132. Power connector 3008 andencoder connector 3010 extend from one side of the actuator. Stator 3002comprises fins 3004 for cooling, structural stiffness and flux pathprovision. As shown in FIG. 129, rotor 3006 is arranged along a centreplane between two stators 3002 each one of which has fins. In FIG. 129,the rotor has an output ring located radially inward from the magnets.Stators 3002 are fixed to housing 3014. Bearings 3016 rotatably connectrotor 3006 to housing 3014, separating inner portions 3018 of actuatorhousing 3014 and a separator ring 3022 separates outer portions 3020 ofthe housing. The bearings as shown are angular contact bearingspreloaded using an approximately constant magnetic force between therotor and stators, which holds the actuator together. Rotor 3006comprises a Permanent Magnet (PM) carrier 3024 and PMs 3012 carried bythe PM carrier 3024. The rotor also comprises an inner ring 3026 fixedto the PM carrier 3024 and connected to inner housing ring 3026 bybearings 3016. The inner ring 3026 comprises an output ring 3028 towhich an element that is to be rotated by the actuator may be connected.The output ring causes such an element to rotate relative to anotherelement connected to fixed ring 3050. The bearings 3016 are mountedbetween two races, in this embodiment an inner diameter race 3052connected to inner portion 3018 of housing 3014, and an outer diameterrace 3054 connected to the rotor 3006. The PM carrier 3024 is made of asoft magnetic material such as an iron alloy or a steel alloy and ismagnetized by an array of permanent magnets in the slots (slots shown inFIG. 132). The stator is made of a soft magnetic material such as aniron alloy or a steel alloy. Soft magnetic materials with high fluxsaturation density are typically very dense. In order to reduce theweight of the actuator an embodiment of an electric machine uses lowdensity materials for the inner and outer housing rings and separatorring. Materials which can be used include aluminum alloys, magnesiumalloys, or composite materials such as carbon fiber composite.

Where a shaft rotates inside a housing the conventional bearingarrangement would have the rotor (rotating shaft) supported by the ID ofthe bearings and the housing (external static structure) supporting theOD of the bearings. Bearing preload would be provided by mechanicalmeans such as a threaded nut or a bolted clamping ring acting on eitherthe ID or the OD of the bearing, and typically in a way that attempts tomove the bearings closer together. If a conventional bearing arrangementwere to be applied to the preferred embodiment, it would therefore havethe rotor attached to a shaft that connects to the ID of the bearingsand the axial magnetic force carried by the housings would act to movethe OD of the bearings closer together. With the bearing outer racesbeing pushed axially together the bearing inner races would reactagainst the applied load with outward acting axial forces; the resultingorientation of the lines of action through the bearings is known as a“face-to-face” configuration. When a pair of bearings has a shortdistance between them, say less than the bearing diameter (as is thecase for the embodiment of FIG. 128 to FIG. 135 and FIG. 138 to FIG.140), a “face-to-face” orientation of the lines of action of the bearingpreload results in a shaft assembly with a much lower moment carryingcapacity than a “back-to-back” arrangement. By mounting the shaft of therotor on the bearing OD's and reacting the inward acting forces of thehousings at the bearing ID's (in the less obvious arrangement), aBack-to-Back line of action bearing configuration is achieved which, incombination with an adequately axially flexible housing, enables themagnetic attraction of the rotor and stator to apply a preload to thebearings in a way that results in a wide separation between the bearingparallel lines of action, thereby maximizing the shaft stability for agiven bearing axial separation distance.

FIG. 130 is an isometric section view of a stator 3002 and housing 3014assembly of the actuator of FIG. 128 with a partial section of layeredconductors 3030. As shown in FIG. 130, the stator has posts 3032according to an embodiment of an electric machine on the left side andspiral flux path cooling fins 3004 on back surface of stator. The statormay be made from one piece of an isotropic material such as an ironalloy or a steel alloy. Spiral cooling fins 3004 may be at least partlymade from the same piece of isotropic material and are primarilycircumferential in orientation in order to provide circumferentialrigidity and flux linkage functionality in addition to increasingsurface area for cooling.

FIG. 131 is an axial view of a stator 3002, inner housing 3018, outerhousing 3020, and exemplary layered conductors 3030 of the actuator orFIG. 128. Connections between phases of the conductors are not shown.Layered conductors 3030 are arranged around posts 3032.

FIG. 132 is an isometric view of a concentrated flux rotor post array3024 for the actuator of FIG. 128, and a rotor support ring 3026 towhich the rotor post array 3024 is fixed. The rotor post array 3024includes a back iron 3034 defining radial holes 3036 through the backiron.

The axial flux embodiment shown here is well suited to achieving verysmall air gaps because the rotor which interacts magnetically with thestator does not carry the output load of the actuator. Instead thebearings 3016 are located between the output ring 3028 and the PMcarrier 3024, so variations in output load will have a minimal effect onthe axial position of the PM carrier relative to the stators. Thestators in this embodiment are held at a precise axial spacing by anaxial spacer ring on the OD of the actuator that prevents axial movementof the stators relative to each other. This structure enables the deviceto achieve and maintain an air gap of 0.005″ for the smallest averageairgap diameter actuator in each boundary. It is believed by theinventor that a 0.005″ airgap will be achievable for motors that arelarger or equal to than the smallest motor in each of the boundaries.The desired airgap for a particular motor will best be determined withconsideration to the application and the given manufacturing tolerances,as well as the loads to be encountered by the structure.

Referring now to FIG. 133, the embodiment has a concentrated flux rotorwith parallel sided PM's 3038. It has been shown that tapered magnetsare able to provide higher torque, but the simplicity and lower cost ofusing parallel sided magnets makes this the preferred embodiment formany applications. Pre-magnetized PM's may be inserted individually intothe slots, or a magnetic material can be injected, poured, or otherwiseinserted while in a non-solid state. It may be possible to thenmagnetize the PM material by applying very high flux density to therotor poles.

The back iron of the rotor between the two PM arrays, is preferablyconfigured to magnetically retain the PM's into the slots. Thissimplifies the assembly process and eliminates the need for a mechanicalPM retention feature on the rotor. The rotor can be configured with thePM's on one axial side aligned with PM's of the same tangential polarityon the other side. Alternatively, the PM's on either side of the rotorcan be of opposite tangential polarity. In this exemplary embodiment,the axially aligned PM's are of opposite polarity to provide a magneticretention force toward the rotor centre plane. To prevent more flux thannecessary for positive PM retention from linking across the backiron, aradial hole 3036 is provided in the back iron and between posts; tocreate a flux path restriction between rotor posts through the back ironwhile still maintaining a rigid post and backiron structure. An array ofaxial holes (not shown) toward the inside of the rotor posts providesanother flux leakage restriction while maintaining a rigid post andend-iron structure.

A set of angular contact bearings 3016 is used to support the rotor inthe housing with the housing fixed to the inner races and the rotorfixed to the outer race. With high strength magnets such as NdFeB 52,the total attraction force between a stator and rotor can be over 400 Kgfor a 175 mm average airgap actuator with a 0.005″ gap. This force ispresent at all times and the total force will does not change by morethan 10% during powered operation due to simultaneous attraction andrepelling of the rotor posts resulting from the alternating polarity ofthe electromagnetic stator poles. This immense attraction force must besupported to create and maintain the desired airgap. The preferentiallysmall airgap of motors inside the disclosed range requires a more rigidstructure than motors outside the disclosed range. At the same time, thethinner backiron that is possible with motors in the disclosed range andthat is necessary to get the full torque-to-weight benefit of thedevice, requires that a more rigid structure is achieved with an axiallythinner stator even though these are two inherently competingcharacteristics. To achieve the required rigidity, embodiments of thedevice use a central rotor with equal magnetic forces pulling on bothaxial sides, and a set of stators on both sides of the rotor which arerigidly connected at their OD's by a separating ring 3022. Theseparating ring on the OD prevents the outer regions 3020 of the statorsfrom closing the airgap, while the angular contact bearings 3016 preventthe inner regions of the stators from closing the airgap.

In addition to the rigidity of this structure, this embodiment providesa consistent preload on the bearings by allowing enough flexibility inthe stators and/or end plates of the housing, that the axial force ofthe rotor attraction with the stators provides adequate preload on thebearings to eliminate bearing play and to keep the bearings preloaded upto a pre-determined design limit for a cantilevered load.

In some cases, the magnetic force of the bearings will be adequate for amaximum cantilevered load. In other cases the bearings may requirehigher preload than is provided by the rotor. In other cases, the forcesgenerated by the rotor may be greater than is necessary or desirable forthe bearings. If the rotor forces are well suited to provide preload onthe bearings, then the housing is preferably configured so the assembledrotor and housing, minus the PM's in the rotor, results in the housingcontacting but not preloading the bearings. The housing is thenpreferably constructed to allow enough elastic deflection of thehousings in the axial direction such that the bearings become preloaded.

If this preload is not adequate to withstand the maximum designrequirement for cantilevered loads, the housing can be constructed toprovide an initial mechanical preload on the bearings with the magneticforce then increasing this preload when assembled.

If the magnetic force would provide more preload than is necessary ordesirable for a given bearing, the housing can be designed to assemblewithout the PM's installed in the rotor such that the housing must beelastically deflected to apply an axial load on the bearings. In thiscase, part of the magnetic rotor force will create contact between thedeflected housing and the bearings, and the rest of the magnetic forcewill provide the desired preload of the bearings.

It is desirable to provide a structure which is very light weight andrigid enough to provide a consistent airgap under these immense forces.By using the magnetic force to preload the bearings, the need forfasteners is reduced or eliminated. This simplifies the manufacturingand assembly and reduces the complexity and weight of the actuator. Thefins 3004 allow the volume of stator material, which can be made of ironor steel or a steel alloy, to be supported by components comprising alow density material such as magnesium, aluminum or a compositematerial. The stator and housing material can be fastened together withbolts or adhesive but are preferably positioned by alignment features inthe housing and stator and held in relative position to each other atleast partially by the magnetic force of the rotor. The housing willinclude a member between the stator and a bearing that is lower densitythan the stator (e.g. inner housing 3018), and which includes a featurewhich prevents the stator from moving in the direction of the rotor toclose the airgap. In an embodiment, this housing member does not have afeature to prevent movement of the stator member away from the rotorbecause it would add weight and cost and it may complicate the assemblyprocess.

If the magnetic force is not sufficient to provide adequate preload onthe bearings at all times during operation, a housing member on the ODof a stator member is provided with a feature (not shown) that aligns onthe stator and prevents movement of the stator member axially away fromthe rotor. This member may be secured to a similar member, such as alongthe center line of the actuator, which is pulling in toward the rotor onthe opposite side of the rotor. These two housing members can be securedtogether with bolts or threads or with an adhesive or a press or snapfit. The stator and/or rotor are preferably constructed with an airgapsurface shape, such as a conical surface shape which allows the outerhousing members to pull the OD of the stators toward the rotor beforethe housing members are fixed together, and which results in aconsistent airgap along the radial distance of the airgap, or a taperedairgap along the radial distance of the airgap between the stator androtor to allow a smaller airgap toward the axis of the actuator. Thesmaller airgap toward the axis allows inner portions of the stator androtor to be axially closer than outer portions of the rotor and statorwithout the inner portions contact sooner than outer portions whenforces on the rotor and/or stator would act to close the airgap. Thistaper does not allow more movement of the outer portions of the statoror rotor, but they do allow a smaller airgap for the inner portionwithout concern for premature contact of these smaller airgap areas.

In order to provide a housing structure that is rigid enough to maintaina consistent airgap yet flexible enough to allow the Rotor PM's toprovide the desired bearing preload, it may be beneficial to constructthe OD connecting ring 3022 to allow a level of axial movement orflexibility between the two stators in this exemplary embodiment. Thiscould be done with a bellows or other somewhat disk or slightly conicalor other similar shape that prevents relative rotation of the twostators while allowing the required magnitude of relative axial movementbetween the stators. This flexible member or assembly can be axiallybetween the stators, or in line with the stators. Very little axialmovement is needed, and is preferably enough to allow the requiredpreload to be applied to the bearings as a result of magnetic attractionin the airgap over the full range of manufacturing tolerances and thechanges in relative axial distance between the stators as a result ofheat expansion in the actuator.

In the exemplary embodiment in FIG. 128, the force of the magnets hasbeen calculated using FEMM software. This attraction force results in anaxial deflection of 0.010″ when the bearing is not present in theassembly. This is considered, by the inventor to be adequate flexibilityto achieve a consistent preload of the bearings over a reasonable rangeof manufacturing tolerances and dimensional changes due to heatexpansion, both of which can be expected to be less than a maximum of0.002″ per bearing interface for a device of this size and usingreasonable machining tolerances.

If the magnetic force pulling the stators inward is more than isdesirable for preload on the bearings, a housing member on the OD of astator member is provided with a feature that aligns on the stator andprevents movement of the stator member axially toward the rotor. Thismember, e.g. separator ring 3022, may be secured to a similar member,such as along the center line of the actuator, which is also pushing theopposite stator away from the rotor on the opposite side of the rotor.These two housing members can be secured together with bolts or threadsor with an adhesive or a press or snap fit or they can be friction fitor simply pressed against each other, or the separating ring. As shownin FIG. 134 they can also be a single component; they can also be anextension of the stators. The stator and/or rotor are preferablyconstructed with an airgap surface shape, such as a conical surfaceshape which allows the outer housing members to push outward on the ODof the stators away from the rotor before the inner housing members arefixed together, such that it results in the desired airgap between therotor and stator after assembly with the PM's in the rotor pulling thestators toward the rotor.

Elements of the above construction can be applied to a single rotor andsingle stator, or two outer rotors on either axial end of a central twosided stator. Elements of the above construction can also be applied toan external output ring configuration with the axially outer membersrigidly fixed together inside the ID of the stator/s.

Heat dissipation benefits of the exemplary embodiment in FIG. 128 toFIG. 135 and FIG. 138 to FIG. 140 is according to the principles of anembodiment of an electric machine. The slot density and conductor volumeis within the boundary for the size of this device where the conductionof heat from the conductors to the back surface of the stators iseffective enough to allow unusually high current density for a givencooling rate applied to the back surface of the stators. Cooling of theback surface of the stators can be done by a number of methods thatinclude radiant, conductive, and convective. Cooling fins 3004 increasethe surface area on the back surface of the stator as well as thesurrounding housing. If the cooling fins are one-piece with the statorand angled along a non-radial line or curve, the fins can be used as aflux path 3040 as shown with the series of arrows in FIG. 135.

It is desirable to maximize the flux carrying capacity of the backironrelative to the weight of the backiron. By angling the cooling/fins tothe posts such that a fin is axially aligned with two or more posts, andby constructing the fins of a soft magnetic material, such as if theyare one piece with the posts and/or backiron, the fins can be used forthree separate functions. Specifically, a fin can, in this way, be usedfor

A). Radial and circumferential strength and rigidity

B). To increase surface area for cooling, and

C). As an integrated flux path member. Using the cooling and/or rigidityfins to enhance the flux path makes efficient use of the high densitystator backiron material to achieve low overall weight.

FIG. 136 shows a simplified section of cooling/structural fins on theback surface of the stator which are preferably one piece with thestator and are more than 50% aligned radially (that is, they are lessthan 45 degrees from radial alignment) at an angle of less than 45degrees to the stator posts. This allows them to perform an additionalfunction of providing a flux linkage path 3040 between posts as shown byarrows. Hatched cross sectional area 3042 indicates a larger distancethrough which the flux passes in the fins between posts due to the finsbeing close to axial alignment in this embodiment and the flux linkagepath 3040 extending diagonally between posts.

In some configurations, such as the embodiment of FIG. 128 to FIG. 135and FIG. 138 to FIG. 140, the stator is supported on the ID and OD whilethe posts provide adequate radial stiffness of the stator itself. Inthis case embodiments of an electric machine use a series of concentricfins and grooves that can provide similar cross sectional area for fluxlinkage from post to post through the backiron, as compared to a 50%thick backiron with no fins, but the fins and grooves provide threeadditional benefits. The first is the potential for dramaticallyincreased cooling surface area on the back surface of the stator. Thesecond is increased rigidity in the circumferential direction. This is abenefit for the configurations where there is a small difference betweenthe number of stator and rotor posts (resulting in a 40-50% forcevariation over a 90 deg angle) and where the backiron would otherwise bethin enough to allow higher circumferential deflection than is desirableas a result. By integrating a series of concentric cooling fins into thesolid stator material, the circumferential stiffness can be increasedwithout increasing the weight of the stator. A third benefit of thisconstruction is a pseudo-laminated effect in the backiron where themultiple thin sections will reduce the eddy current production in thestator back iron between posts. There may be a slight increase in thereluctance across the backiron due to a longer flux path, but thebenefit in terms of reduced eddy currents is expected to partially orcompletely offset this detriment.

In the simplified exemplary section shown in FIG. 137, the maximumbackiron thickness (i.e. including the full heights of the fins) isapproximately twice that of a hypothetical non-finned backiron with 50%the thickness of the posts). It has approximately the same crosssectional area, however, so it is expected to have similar magneticreluctance. In this way, the surface area available for heat extractioncan be many times more than the non-finned surface area for much moreeffective cooling, but without compromising the weight or the magneticproperties, and at the same time providing the additional benefit ofincreased circumferential rigidity. In the embodiment shown in FIG. 137,cooling fins 3454 are integrated into the stator 3450 in a directionwhich is not aligned with the posts 3458. The fins may be tapered. Oneor more of the cooling slots 3456 may be deep enough to create anopening in the root of the stator post slots 3452. The back ironincluding the fins may have a height greater than 50% of the post width.The opening in the stator slot allows the conductor to be cooleddirectly by a cooling fluid or heat dissipating member (not shown)through conduction. Air or a cooling fluid may pass through the openingaround the conductors and through the intersection of the cooling slotsand post slots, either into or out of the actuator. Movement of thecooling fluid may be by forced convection or by natural convection as aresult of heating of the conductors and stator. In an embodiment, thestator is made of a soft magnetic material such as, but not limited to,steel or steel alloy, or iron or iron alloy, and fused together with anon-magnetic material, such as aluminum or magnesium alloy, along afused line or a gradual transition, such as by explosion welding, oradditive manufacturing, such as 3D printing and sintering. Cooling finsare then cut into the back surface of the stator. This providesincreased surface area while the fused-on material forms fused fin tips3460 which may be of lower density and higher heat conductivity than theremainder of stator 3450. Fastening protrusion 3462 Is provided at edgeof stator 3450 perpendicular to the stator posts for securing to thehousing (not shown).

Motors inside the disclosed boundary are characterized by unusually lowconductor volume and unusually high slot density which results in lowheat flow resistance from the conductors to the back surface of thestator.

In addition to the inherent heat dissipation benefits inside thedisclosed range, it is possible to increase the heat extraction from theback surface of the stator by the application of one or more of thefeatures described here. It should be noted that a number of thefollowing cooling system features could be applied to any motor in theseries including motors outside of the disclosed range. The applicationof one or more of these cooling system configurations with geometryinside the disclosed range, however, will result in higher performancein terms of continuous torque density, because the heat flow resistancefrom the conductors to the back surface of the stator is limitingfactors in all of these motors, and an inherent benefit of motors insidethe disclosed range is low heat flow resistance from the conductors tothe back surface of the stator.

If a given cooling rate is applied to the back of the stator, it willenable the extraction of a certain number of watts of heat from thedevice based on the surface area, cooling rate and the temperaturedifference between the stator and the cooling fluid. Specifically, thereis a proportional relationship between the surface area contacted by thecooling fluid and the number of watts of heat extracted if all othervariables are held constant. Therefore, neglecting any changes totemperature gradients within the heated structure, any increase insurface area will result in a roughly proportional increase in theamount of watts of heat dissipated from the structure. If the surfacearea is increased by 10× by the addition of fins, it would be reasonableto expect that significantly more heat will be extracted for the samecooling rate. Conversely, for a finned surface to dissipate the sameamount of heat as a non-finned surface with all other variables heldconstant, it will only require a fraction of the cooling rate.

Cooling of the embodiment of FIG. 128 to FIG. 135 and FIG. 138 to FIG.140 (with fins integrated into the stator) is preferably accomplishedwith a solid stator made from a solid soft magnetic material such as,but not limited to steel or iron or a steel alloy such as a cobaltalloy, or nickel alloy or a sintered soft magnetic powder material suchas but not limited to ferrite powder or a cobalt iron powder material orpossibly other soft magnetic materials existing or not yet existing.Laminated electrical steel may also be used but is more challenging toachieve a strong and rigid structure due to the mechanical limitationsof the adhesives used between the layers combined with the thin sectionsthat are necessary to achieve high torque density. This is especiallytrue at elevated temperatures where adhesives tend to lose part of theirstrength. The constant loading of the stator as a result of the magneticforces between the rotor and stator makes creep deformation of theseadhesives a significant issue that must be avoided. A stator made of100% laminated material will have a high stress-concentration on theadhesive between the layers and is, therefore, considered by theinventor to be less structurally sound than a solid metal or sinteredmetal stator as shown here.

Using the magnetic attraction between the rotor and stators providesconstant preload on the bearings and reduces or eliminates the need forfasteners or adhesive to hold the actuator together. In someapplications the magnetic force may be greater than necessary to preloadthe bearings at all times. In other applications the magnetic forcebetween the rotor and state or may not be adequate to preload thebearings at all times. FIG. 138 shows a configuration of the embodimentof FIG. 128 whereby the axial faces of the separator ring will contactthe axially facing surfaces of the outer housing before the innerhousing axial faces contact and preload the inner races of the bearings.That is, before assembly bearing-housing gap 3044 is larger thanseparator ring-housing gap 3046. This structure will relieve some of thepreload which results from magnetic attraction between the rotor andstators through elastic deformation of the housing and stators.

In FIG. 139 the axially facing surfaces of the inner housing contact theaxial surfaces of the inner races of the bearings before the axialsurfaces of the separator ring and outer housings contact. That is,before assembly bearing-housing gap 3044 is smaller than separatorring-housing gap 3046. This configuration can increase the preload onthe bearings beyond that provided by the magnetic force between therotor and stators. This configuration will, however, require mechanicalor adhesive fastening of the outer housings 3020 and separator ring3022.

Shown in FIG. 140 is a cross sectional view of an embodiment with sealedfluid passages 3048 on the back surface of the stators 3002 such ascould be used for fluid cooling such as gas or liquid cooling.

Referring to FIG. 140A there is shown an embodiment showing the flow offluid in fluid passages in housing 3472 of machine 3470. Cooling fluidenters an outer semi-circular passage 3474 through cooling fluid input3476. Cooling fluid flow 3492 is shown by arrows. A fluid passage 3490allows fluid flow to move from outer semi-circular channel 3474 to innersemi-circular channel 3478. Fluid flow then exits inner semi-circularchannel 3478 through cooling fluid output 3480.

Referring to FIG. 140B and FIG. 140C, there is shown an embodiment ofactuator 3770 with a rigid connection 3488 between two housing halves3472 around the inner diameter of the actuator. The outer diameter ofthe housing 3472 includes attachment features 3486. In operationattractive magnetic forces produced by the stators 3482 and rotor 3484press the two housing halves together in an axial direction. The rigidconnection 3488 maintains the rigidity of the structure at the innerdiameter. In the absence of further supporting structures or otherpoints of contact, such as bearings, the air gap between rotor andstators could be closed by these attractive magnetic forces.

Concentrated Flux Rotor with Structural and Assembly Features

Aligned Permanent Magnet Rotor

A known permanent magnet rotor configuration uses magnets that arepolarized in the direction of the flux path. This type of rotor uses asoft magnetic back iron by providing a flux linkage path betweenadjacent opposite polarity magnets. Soft magnetic materials arematerials that are easily magnetised and demagnetised. The flux linkagepath in the back iron decreases the flux density in the airgap and alsoresults in a magnetic attraction between the permanent magnets and theback iron to reduce or eliminate the need for an adhesive or mechanicalfixture to hold the magnets in place during operation.

An embodiment of an electric machine can be used with an alignedpermanent magnet rotor in all of its various configurations.

Concentrated Flux Rotor

Concentrated flux rotors use tangentially polarized magnets ofalternating polarity, and are known, to someone skilled in the art, asproviding the potential for higher flux density in the rotor posts atthe airgap than is possible if the same magnets were used in an alignedPM configuration.

A concentrated rotor is comprised of an array of tangentially polarizedalternating polarity magnets which are separated by an equally numberedarray of soft magnetic material flux concentrating rotor posts. Therotor is preferably made from one piece of isotropic or homogenous steelor iron alloy and is constructed such that there is a rigid connectionof material between adjacent posts with the rigid connection beingpreferably made of the same isotropic or homogenous material such as acast part or a part that is machined from the same isotropic blank suchthat it requires minimal or no adhesive between the posts and connectingmaterial. A material is isotropic if it has the same structuralproperties in all directions. A material is homogenous if it has auniform composition throughout. If the rotor is double sided (such aswith a central rotor axial motor with a stator on both axial ends of therotor) there may also be a rigid connection between a post on one axialside of the rotor and a post on the other axial side of the rotor, withthe rigid connection being preferably made of the same isotropic orhomogenous material such as a cast part or a part that is machined fromthe same isotropic or homogenous blank. Losses from flux leakage pathfrom post to post that is created by this rigid connection may bereduced by an electric machine within the ranges of pole pitch and postheight disclosed.

One of the keys to maintaining torque with an embodiment of an electricmachine, while providing a sufficiently rigid isotropic structure is touse a combination of permanent magnet magnetic strength and permanentmagnet depth that is deeper than is necessary to saturate the rotor posttips. Permanent magnet depth is defined as the axial length of thepermanent magnets when in an axial flux configuration, and the radiallength of the permanent magnets when in a radial flux configuration.Permanent magnet width is defined as the tangential length of thepermanent magnet for both radial and axial flux configurations.Permanent magnet length is defined as the axial length of the magnet inradial flux configurations, and the radial length of the magnet in axialflux configurations. Once the tips of the rotor posts are saturated anyadditional PM depth will provide diminishing benefit in terms of torque.Embodiments of an electric machine use a magnet depth that is deeperthan necessary to saturate the rotor post tips at the airgap so theadditional flux which leaks though the back iron has a minimal effect onthe torque. In addition to the increased magnet depth, embodiments ofthe electric machine may use one or more flux path restrictions in theflux leakage path to reduce flux linkage through the back iron.

In addition to the internal stresses produced by the repelling forces ofthe PMs and saturated posts, the axial forces created by high strengthPM's, such as N52 magnets, combined with this structure, can, for a 175mm average air gap actuator of an embodiment of the present device,exceed 400 kg. Retaining elements, which may variously be back irons,side irons or end irons, provide additional structural rigidity that mayallow the use of a smaller air gap

Embodiments of the disclosed electric machine provide very high fluxdensity at the air gap end of the rotor post as a result of aconcentrated flux configuration. Furthermore, some embodiments of anelectric machine provide for the permanent magnets to be held in placeby their own flux to reduce or eliminate the need to rely on an adhesiveto secure the magnets to the rotor posts.

Embodiments of an electric machine take advantage of a solid connectionbetween two or more posts of the stator by the use of a back iron. Thisback iron has the apparent disadvantage of creating a short circuit forsome of the PM flux that would otherwise link across the air gap toprovide torque, but it has been shown by analysis and testing thatcertain geometric considerations disclosed here allow for a minimal lossof torque even though a high percentage of permanent flux is allowed toleak from one magnet post to the next through the back iron.

The use of sufficient back iron is beneficial to provide structuralstrength and rigidity to withstand the immense forces generated by theflux linking across the air gap. When constructed as one piece with asolid iron or steel alloy connection between rotor posts, analysis hasshown that embodiments of the electric machine having the disclosed polepitch and post height areable to maintain a consistent air gap includingdown to air gaps of 0.005″ or smaller for a 175 mm average air gapdevice. The following configurations of an electric machine withconcentrated flux rotor provide a sufficient percentage of flux in theair gap despite high flux linkage through the back iron from theopposite end of a post to the opposite end of an adjacent post.

Deep Magnets with Back Iron

Referring to FIG. 141, there is shown a rotor 3300 and stator 3330 of anembodiment of the present device. The rotor includes rotor posts 3304and back iron 3310 form a continuous structure. Rotor posts 3304 andback iron 3310 are formed from a homogenous and isotropic material, inwhich the rotor posts 3304 are homogenous extensions from the back iron.The spaces between rotor posts 3304 define rotor slots 3306. Rotor slots3306 are filled by permanent magnets 3302. The stator 3330 includesstator posts 3332 and conductor layers 3334.

Permanent magnets 3302 have a magnetic saturation depth at which the endof the rotor posts 3304 are saturated at the air gap 3308 and additionalmagnet depth 3336 would not significantly add to the flux density in theair gap 3308. Beyond this permanent magnet depth it has been found thatthe use of a back iron has a decreasing and then minimal effect on theflux at the airgap. At a 1:1 magnet depth to magnet width ratio, theback iron has a significantly detrimental effect on the flux density atthe airgap. At ratios of 2:1 and 4:1 there are successively smallerlosses of flux density across the airgap.

FIG. 141 also shows the permanent magnet width 3338, as defined above,rotor post depth 3340, and the stator post depth 3342. The rotor postdepth and stator post depth are defined as the length of the rotor orstator post in the axial direction when in an axial flux configurationor the radial direction when in a radial flux configuration.

To provide sufficient structural strength and stiffness, embodimentsemploy a magnet depth that is longer than would be necessary for maximumair gap flux density. These over-depth magnets require rotor posts thatare longer than would be necessary without back-iron, which results inan axially longer rotor structure when in an axial configuration withthe effect of increasing the strength and stiffness of the rotor. Inaddition, embodiments include a soft magnetic back iron which ispreferably one piece with the post members. In combination with theextra axial post length, the back-iron feature provides a one-piecerotor post array construction with very high strength and rigidity.

In addition to the increased length of the rotor posts; which increasesthe strength and stiffness of the rotor, a secondary benefit of theover-depth magnets is the highly saturated rotor posts at the air gap.As a result and in combination with the small air gap, a thick back ironfor structural rigidity and strength can be used without dramaticallyreducing the flux density at the air gap.

Embodiments of the device provide additional depth of the PM's and rotorposts to contribute to the necessary rigidity. At the same time, theadditional depth of these PM's enables a rigid connection between rotorposts with a preferably one-piece magnetically soft back iron betweenrotor posts without dramatically affecting the flux density at the airgap.

One of the reasons a person skilled in the art would expect a back-ironfeature to be a detriment on a concentrated flux rotor would be theexpectation that a high percentage of flux from the magnets would linkfrom post to post through the low reluctance flux path of the back ironinstead of linking across the high reluctance flux path of the air gap.One of the effects of the back iron, however, is to provide high enoughstrength, rigidity and creep resistance that a very small air gap can beachieved, even with the very high magnetic forces created by thisconstruction. By enabling air gaps down to 0.005″ or lower, thereluctance of the air gap can be unusually low, making the flux linkagepath through the back-iron less detrimental than would be expected witha larger air gap.

For applications where maximum flux density is desired, and where aconcentrated flux rotor requires the high strength and rigidity providedby the use of one-piece construction including a back iron component,increasing the depth of the PMs and the rotor posts increases the fluxdensity in the air gap to equal or exceed the flux density of the airgap with shorter permanent magnets and no back iron.

In this way, this embodiment of the present device provides a highstrength, high mechanical rigidity concentrated flux rotor by the use ofa unified soft magnetic material post array and back iron and it doesthis with minimal reduction of the air gap flux density through the useof increased magnet depth and post height.

Magnet Retention with Back Iron Structure

Referring to FIG. 142 to FIG. 143, embodiments of the device use a rangeof geometric features and parameters that provide a flux linkage paththrough the back iron to provide a magnetic force working to retain thepermanent magnets including in conditions of high current and nocurrent. Magnetic flux passing through the back iron creates a magneticforce that attracts the magnets into the slot therefore helps to retainthe magnets. To ensure that permanent magnets are magnetically retainedagainst the bottom of the slots at all times the geometry of someembodiments of the device is such that the total magnetic flux thatlinks through the rotor posts and back iron is higher than the flux thatlinks across the air gap. It is also preferable under a variety of otherinfluencing conditions that the total magnetic flux that links throughthe rotor posts and back iron is higher than the flux that links acrossthe air gap when the stator is powered at maximum current.

There are a variety of ways to bias the flux linkage through the rotorrather than the air gap. Some non-limiting examples are shown here.Other methods of magnetically retaining the PM's in the slots arepossible. Any construction that provides greater flux linkage throughthe rotor back iron than across the air gap has the potential to providea magnetic retention effect on the magnets. It may be preferable to usean adhesive to secure the magnets in the slots, but the purpose of theadhesive is, in this case, not to prevent dislodging the magnets, butrather to prevent vibration of the magnets during operation.

Tapered Slots

It is also possible to provide force to retain the magnetics in therotor slots using a combination of mechanical and magnetic force.Tapered magnets can provide a structure in which a significantpercentage of magnetic flux goes through the airgap while retaining themagnets in the rotor slots.

Magnets which taper tangentially such that they are thinner toward theair gap, can provide high performance in a concentrated flux rotorconfiguration. Referring to FIG. 144 there is shown a rotor 3300 in anaxial flux configuration with magnets 3302 having tapered ends 3316 androtor posts 3304 with tapered ends 3318. The magnets and rotor poststaper in opposite directions to form an interlocking arrangement.Permanent magnets taper in the direction of the stator 3330 while rotorposts 3304 taper away from the stator. In this embodiment twosubstantially mirrored rotors 3300 can be assembled between a pair ofstators, with tapered posts of each rotor meeting back to back andtapered magnets of each rotor meeting back to back. Tapering the magnets3302 in this way, allows for greater rotor post width at the air gap3308. It also allows for greater magnet width 3338 at the wide end ofthe magnet taper to provide more flux to the rotor post 3304 away fromthe air gap 3308, where if the sides were parallel the posts 3304 wouldtend to be less saturated. In this way, the active permanent magnet 3302and soft magnetic materials are used more effectively to provide moreflux at the airgap 3308. The two rotors parts can be secured togetherfor example by an adhesive, but in some preferred variations amechanical feature such as bolts (not shown) or a securing ring (notshown) may be used.

The interlocking arrangement of tapered posts 3304 and magnets 3302prevents the permanent magnets from dislodging, which reduces the needfor magnetic force to retain the magnets in the rotor, and thereforereduces the need for magnetic flux to leak through the end iron 3314.

In some embodiments an array of flux path restrictions 3328 can beformed in the end iron 3312, for example, as holes in the end iron 3314at the base of each rotor 3304 where they connect with the end iron3314. These flux path restrictions 3328. These flux path restrictions3328 reduce the available flux path between rotors 3304 and end iron3314.

FIG. 144 shows an axial flux configuration of a tapered slot rotor, butthe tapered slot rotor can be equivalently constructed in a radial fluxconfiguration. Tapered magnets may narrow towards or away from theopposing carrier.

A second effect of tapering the magnets in this way is to bias a highpercentage of the flux from a permanent magnet toward the air gap. Thisis beneficial in at least two ways. A first is that the taperedpermanent magnet will be drawn toward the air gap where they will closethe airgap between the permanent and the rotor slot wall for lowerreluctance flux linkage and where they will be mechanically preventedfrom further movement and therefore securely retained by the taperedrotor posts. Secondly, the narrower rotor posts at the back surfaceresults in a greater distance from post to post along the center planeof the rotor. This reduces the amount of leakage through the air frompost to post along the center plane of the rotor. By assembling twosubstantially mirrored rotor halves with tapered posts and taperedmagnets back-to-back a large percentage of the flux from the permanentmagnets can be forced to link across the air gap.

In this way, very high flux density can be achieved in the air gap whilemagnetically and mechanically retaining the magnets. A cost effectiveway to manufacture a tapered rotor post rotor is to use two symmetricalrotors 3300 back to back. This construction does not allow for the useof a back iron 3310 to stiffen the rotor, so a soft magnetic end iron3314 is used instead. The end iron 3314 has sections that are preferablyas thin as possible to create a high reluctance flux path between rotorposts through the end iron, and as thick as necessary to provide themechanical strength and rigidity to maintain a small and consistent airgap.

To compensate for the loss of flux from post to adjacent post throughthe end iron connection, an embodiment uses permanent magnets 3302 thatare longer than the soft magnetic stator posts 3332 at the air gap 3308.This is shown in FIG. 145 where the permanent magnet 3302 is shown asbeing longer than rotor posts 3304 which would have the same or nearlythe same length as the stator posts 3332. By increasing the permanentmagnet depth 3336 compared to the stator radial length, the permanentmagnets 3302 will be adequate to saturate the end iron 3314 while stillmaintaining high flux density in the rotor posts at the airgap.

Manufacturing methods for the rotor can include casting or forming orpowdered metal construction, additive manufacturing, machining etc.Manufacturing of the magnets can be done by forming or additive orsubtractive manufacturing. Magnets can also be magnetised afterinsertion into slots. It may be possible with present or futureprocesses to press powdered hard magnetic material into the rotor slotsand then magnetizing the PM material after pressing, or a slurry of PMmagnet material in an epoxy or other polymer can be used to fill theslots and then magnetized after hardening. Magnetizing of the hardmagnetic material can be done by applying very high flux density to twoor more posts at a time.

Back irons, side irons and end irons serve as retaining elements andform a rigid connection with the rotor posts. Features of one embodimentmay be combined with features of other embodiments.

Exemplary Concentrated Flux Rotor Configurations:

Referring to FIG. 146 and FIG. 147, there is shown an angled sectionview of an embodiment of a concentrated flux rotor in a radial fluxconfiguration. Rotor posts 3304 include an rotor relief 3320 whichprevents the magnet 3302 from moving radially out of the rotor slot3306. The rotor posts 3304 are connected by side iron 3312 (not shown inFIG. 146, but see FIG. 147). Side iron 3312 creates a flux linkage paththat allows magnetic flux to pass through side iron 3312 and create anattractive magnetic force between the permanent magnet 3302 and the sideiron 3312. The combination of the side iron 3312 and rotor relief 3320positively retains permanent magnets 3302 in the rotor 3300. In thisembodiment, part of the rotor post 3304 is relieved to help retain themagnets in the bottom of the slot (radially outward in this case) and amagnet securing

FIG. 148 shows an angled section view of concentrated flux rotor posts3304 and side iron 3312 in combination with mills that may be used toform the posts and side iron structure from a single block of material,such as of soft magnetic material. A regular end mill 3370 may be usedto cut a wide recess into the block, working in from the outercircumference of the rotor. A smaller diameter end mill 3372 may be usedto form a recess into which the permanent magnet 3302 can be inserted. Arelieved shaft end mill 3374 can then be used to mill the rotor post3304 to form the rotor relief 3320. The smaller diameter end mill 3372and relieved shaft end mill 3374 can work in from the innercircumference of the rotor 3300. One or more walls may be left at axialends of the block of material to form the side iron 3312.

While FIG. 146 to FIG. 148 show a radial flux configuration, an axialflux configuration variant of this design could be made with equivalentstructures and methods.

Referring now to FIG. 149 there is shown a slot geometry in a schematicFEMM analysis of a linear representation of the rotor of the embodimentshown in FIG. 146 to FIG. 148. FIG. 149 shows the flux paths of two slotgeometries of rotor. The four permanent magnets 3302 on the left side ofthe schematic are rectangular. The four permanent magnets 3302 on theright side of the schematic have a tapered end 3316 which increases themagnetic force retaining the permanent magnets 3302 in the slot. Thismay have the advantage of reducing the need for other methods ofsecuring the permanent magnets in the slot.

FIG. 150 shows an angled section view of embodiment of a rotor 3300 in aradial flux configuration with an end iron 3314. In this embodiment therotor posts 3304 include rotor relief 3320, and tapered rotor post ends3318. The tapered rotor post ends 3318 can serve to reduce the weight ofthe rotor 3300. Rotor reliefs 3320 can help retain permanent magnets3302 and in some variations can extend full across the slot to form aback iron 3310, with the effect of providing extra rigidity and helpingto retain the permanent magnets 3302 in the slot by magnetic force.

Referring to FIG. 151 there is shown a stator-rotor-stator configurationwith an end iron 3314. The end iron 3314 and rotor posts 3304 can beformed from a single piece of isometric soft metallic material, with asingle array of permanent magnets 3302 fitting between rotor posts 3304.End iron 3314 is formed at both ends of the rotors 3304. In thisembodiment, flux path restrictions 3328 can be included as shown in FIG.152.

FIG. 152 shows an embodiment of a stator-rotor-stator configuration witha back iron 3310, end iron 3314 and flux path restrictions 3328. In thisembodiment the two array of permanent magnets 3302 are separated by backiron 3310. Flux path restrictions 3328 are formed as bores at the endsof the permanent magnets 3304 to reduce the flux leakage in the end iron3314.

FIG. 153 shows an embodiment of a rotor-stator-rotor configuration. Twoconcentrated flux rotors 3300 engage a central stator 3330. The rotors3300 each include end iron 3314 and flux path restriction 3328. In manyapplications end iron only or back iron only will be sufficient toprovide adequate rigidity to the concentrated flux rotor 3300.

FIG. 154 shows an embodiment of a rotor-stator-rotor configuration. Theembodiment is essentially the same as that shown in FIG. 153 with theaddition of a think back iron 3310 on each rotor 3300.

FIG. 155 shows an embodiment of a trapezoidal stator-rotor-statorconfiguration. Stators 3330 are shown without conductor layers 3334. Therotor 3300 includes a back iron 3310 and end iron 3314 and has a roughlytrapezoidal shape in a cross-section along the cylindrical axialdirection. The rotor is composed of two rotor halves, and thecombination with both a back iron 3310 and end iron 3314 provides highmechanical rigidity to the rotor. FIG. 156 shows a variation of theembodiment of a stator-rotor-stator configuration shown in FIG. 155 withonly an end iron 3314 and no back iron 3310.

FIG. 157 shows an embodiment of a trapezoidal rotor-stator-rotorconfiguration. Stator 3330 are shown without conductor layers 3334. Therotors 3300 include end irons 3314 shown at the inner diameter and outerdiameter ends of the permanent magnets 3302. In this embodiment the backsurface of the rotors 3300 is interlocked with a low density housingcomponent. FIG. 158 shows an embodiment of the trapezoidalrotor-stator-rotor configuration shown in FIG. 157 with a back iron 3310and no end iron 3314.

FIG. 159 shows an embodiment of a rotor-stator-rotor configuration of alinear flux machine. The stator 3330 has an array of posts 3332, noconductors 3334 are shown. The rotor surrounds the stator and is made ofone or more pieces material, for example, a soft magnetic isotropicmaterial. Receiving slots for the permanent magnets 3302 on the internalstructure of the rotor housing 3300 act as rotor posts 3304, rotor backiron 3310 and rotor end iron 3314. Many constructions for a linear motorare conceived by the inventor. The side section of the rotor 3330, forexample, may be of a different material than the upper and lower rotorportions. FIG. 160 shows an embodiment of the rotor-stator-rotorconfiguration of a linear flux machine shown in FIG. 159 without a backiron 3310 on the rotor 3300.

FIG. 161 shows an embodiment of a stator-rotor-stator configuration of alinear flux machine with the rotor 3300 being formed of two arrays ofmagnets 3302 separated by rotor posts 3304 and back iron 3310. As withother concentrated flux rotors, the permanent magnets are alternatingpolarity in the linear direction, and may be the same polarity asopposing magnets on the other side of the back iron or may be oppositepolarity as opposing magnets on the other side of the back iron. Thetraveller in this embodiment may be made of an isotropic soft magneticmaterial. FIG. 162 shows a partially assembled embodiment of astator-rotor-stator configuration of a linear flux machine in which therotor 3300 has end iron 3314 and no back iron 3310. In this arrangementthe permanent magnets stops are used to position the magnets at precislocations in the slots. Permanent magnets in the top and bottom of therotor may be of the same polarity or opposite polarity but arepreferably of the same polarity to reduce flux linkage from top tobottom magnets through the rotor posts. Rotor posts 3304 and end iron3314 may be made from a single piece of isotropic soft magneticmaterial.

It has been shown by FEMM analysis that removing material from part ofthe side of the rotor posts can result in a positive retention force onthe permanent magnets with an additional benefit of reducing the rotormass.

FIG. 163 and FIG. 164 show an isotropic rotor post array with aninterrupted back iron 3310 and a relief 3322 on the rotor post walltoward the center plane of the rotor. In this embodiment, the permanentmagnets are circumferentially polarized and opposite polarity to theaxially aligned counterpart. The effect of this is to retain thepermanent magnets into the bottom of the slots with significant force inthe passive state, even though more than 50% of the flux lines from thepermanent magnet are linking across the airgap. In order to provide anadequately strong and stiff isotropic post and connector member for anembodiment with an interrupted back iron, as shown here, there will needto be an end-iron connector on at least one end of the rotor posts (notshown). The longer the permanent magnets (in the Z axis of FIG. 163) theless effect the end iron will have on the flux in the airgap and thetorque (or force in the case of a linear motor) which can be produced.

Transverse Flux Machine

For application of the disclosed geometry to motor types such astransverse flux motors, there may be other design considerations thatwill affect the extent to which the heat dissipation and otheradvantages in the disclosed range are realized. For a transverse fluxmotor, for example, the width of the posts (in a direction parallel tothe axis of the coil) is independent of the pole pitch. This width,however, affects the weight of the system because it is directly relatedto the necessary thickness of stator backiron. One must also considerthe ratio of the axial width of the post to the axial width of the coil.If these quantities are decreased, the total air gap surface area andconductor cross-sectional area can be held constant by arraying theentire assembly axially. Therefore, the optimum torque-to-weight andheat dissipation will also depend on the array pitch and post axialwidth.

Exemplary Transverse Motor

There are many known variations of transverse flux motors. Shown hereare non-limiting exemplary embodiment of a transverse flux motoraccording to the principles of the present device. Two phases are shownhere although fewer or more phases may be used with different effects.In the first embodiment, shown in FIG. 165 to FIG. 166B the flux linksfrom the rotor to the stator in a somewhat radial direction, butvariations on the transverse flux principle may have flux linkingaxially or at an angle to the axis of the device, for examples, as shownin FIG. 167 to FIG. 169.

Referring to FIG. 165 to FIG. 166B, there is shown an exemplarytransverse flux motor 3410. The transverse flux motor 3410 may have ahousing 3412 and employs two stator halves 3430 and a rotor 3420. Thestator 3430 includes conductor 3432 and stator posts 3434. The conductor3432 as shown comprises circumferential conductor coils but differentvariations for the conductor may be used. In the two phase design shownthere is one conductor coil 3432 per phase, each conductor coil havingmultiple turns. A concentrated flux rotor 3420 may be used as shown inFIG. 166B. The concentrated flux rotor 3420 employs permanent magnets3422 with tangentially polarized alternating polarity. The rotor mayalso include flux restriction holes 3428 and a back iron 3426. The backiron 3426 and rotor posts 3424 may be produced from a single piece ofisotropic soft magnetic material. In this configuration the flux flowacross the airgap between the rotor and the stator is in the radialdirection.

The heat dissipation benefits of the disclosed range are applied to theexemplary transverse flux machine as a result of the low radial distancefrom the OD of the stator posts, to the OD of the circumferentialconductor slot. The high pole density of the rotor corresponds with thesame slot density in the stator as a result of the 1:1 statorpost-to-rotor magnet ratio which is typical of transverse flux machines.

As with many two phase transverse flux machines, the stator posts oneach stator have posts that are offset by half a pitch. The stators arethen offset from each other by ¼ pitch so the motor can deliver constanttorque in either direction by controlling the current to each of the twocoils.

Due to the thin section of the flux path from post to post as a resultof the disclosed geometry, it is believed by the inventor that anisotropic soft magnetic stator material will provide increased torqueand efficiency as compared to the same material in laminate form atspeeds that are suitable for robotics.

Referring to FIG. 167 to FIG. 169, there is shown a transverse fluxmachine with a generally axial flux linkage path across the airgapbetween a rotor and stator. In this configuration a concentrated fluxrotor 3420 is held between two stator pieces 3430 in a housing 3412.Magnetic flux in this configuration flows across the airgap between therotor 3420 and each stator 3430 in an axial direction. In thisconfiguration the rotor 3420 comprises two arrays of magnets 3422, thetwo arrays separated by a back iron 3426 and the magnets in each arrayset between rotor posts 3424. As in the radially directed transverseflux motor, the back iron 3426 and rotor posts 3424 may be produced froma single piece of isotropic soft magnetic material.

General Principles for Some Embodiments

Any of the disclosed structures may be used with an electric machinethat has electromagnetic elements including posts and slots between theposts, where the posts are wound to create poles, at least on either ofa stator or rotor, where the pole density is within a range of poledensity defined by the equations specified in this patent document andthe post height is within a range of post height defined by theequations specified in this patent document. These equations each definea bounded area. The bounded areas are dependent on the size of theelectric machine, where the size is defined by the radius of themachine. The bounded areas together define a bounded surface in a spacedefined by pole density, post height and size of machine. For eachradius of an electric machine, the bounded region is believed by theinventors to be new and unobvious.

Based on modelling studies and FEMM analysis, the inventors believe thefollowing, at least beyond a specific pole density and for a specifiedconductor volume or post height for a given diameter of motor: 1) anelectric machine having pole density and conductor volume or post heightas disclosed has increased heat production (and thus lower efficiency)for a given torque or force as compared with an otherwise equivalentmachine having lower pole density and/or higher conductor volume but hascorresponding effective heat dissipation; and 2) the increased poledensity and lower conductor volume or post height also has the effect ofdecreasing mass as compared with an otherwise equivalent machine havinglower pole density and/or higher conductor volume, with an overallincreased torque to mass ratio (torque density).

An electric machine with increased torque to mass ratio is particularlyuseful when several of the electric machines are spaced along an arm,such as a robotic arm, since efficiency is less important relative tothe need for one electric machine to lift or accelerate one or moreother electric machines. The inventor believes that improved performanceof an electric machine having pole density and conductor volume or postheight as disclosed results at least in part from 1) a narrower slothaving a shorter heat flow path from the hottest conductor to a post and2) a shorter heat flow path from the top of a post to a heat dissipationsurface.

For example, each electric machine embodiment disclosed is shown ashaving a pole density and post height that is within the definition ofpole density and post height that is believed to provide a benefit interms of K_(R).

With a pole density in the range of 0.5 and higher, for example, andconsidering that it is not unusual for a slot to be about as wide as atooth, tooth width can be in the order of 1 mm for a 25 mm wide machine.Narrower teeth can be used. An advantage of thinner teeth is that solidmaterials such as, but not limited to steel or iron or a magnetic metalalloy, may can be used with minimal eddy currents due to the teeth beingcloser to the thickness of normal motor laminations. A common motorlamination for this size of motor can be in the range of 0.015″ to0.025″. The proposed pole density and tooth geometry (many short posts)also helps avoid eddy currents in the first carrier (stator). Forexample, for an electric machine with 144 slots, eddy current loss wasfound to be only 7% of the total resistive losses in the windings at 200rpm and 70 A/mm². Use of solid (non-laminated) materials providesadvantages in strength, stiffness and reliability.

Embodiments of the disclosed machines may use fractional windings. Someembodiments may use distributed windings; another embodiment usesconcentrated windings.

Distributed windings are heavier due to more copper in the end turns andlower power (requiring a bigger motor). They also require thickerbackiron because the flux has to travel at least three posts, ratherthan to the next post as with a fractional winding. Distributed windingsproduce more heat because of the longer conductors (the result of longerdistance the end turns have to connect between).

An embodiment of an electric machine with the proposed pole density mayhave any suitable number of posts. A minimum number of posts may be 100posts. A high number of posts allows fewer windings per post. In anon-limiting exemplary embodiment, the windings on each posts are onlyone layer thick (measured circumferentially, outward from the post).This reduces the number of airgaps and/or potting compound gaps and/orwire insulation layers that heat from the conductors conduct through forthe conductors to dissipate heat conductively to the stator posts. Thishas benefits for heat capacity (for momentary high current events) andfor continuous operation cooling. When direct cooling of the coils bymeans of gas or liquid coolant in direct contact with the conductors, alow number of circumferential layers, and for example a singlecircumferential layer of wire on a post, combined with high poledensity, results in a very high surface area of the conductors (relativeto the volume of the conductors) exposed to the cooling fluid. This isbeneficial for cooling the conductors and is one of many exemplary waysto take advantage of the low conductor volume as disclosed. A single row(or low number of rows) of coils per posts also reduces manufacturingcomplexity allowing for lower cost production. In another embodiment,the windings of each post are two layers thick.

For a 175 mm or more average airgap electric machine, the number ofslots may be 60 or more, or 100 or more for an axial flux electricmachine, for example 108 slots in an exemplary 175 mm diameterembodiment. In addition, for such an electric machine, the averageradial length-to-circumferential width of the posts may be above 4:1,such as about 8:1 but may go to 10:1 and higher. For the exemplary 108slot embodiment, the ratio is about 8:1. With such a configuration, theheat dissipation is improved. A lower aspect ratio would be a lot ofmaterial for very little torque, so the aspect ratio helps achievetorque useful for high KR and robotics while at the same time takingadvantage of the heat dissipation effects.

In an embodiment, an electric machine may be built with a stratifiedconstruction which allows main components to be fabricated from, forexample, sheet stock of conductor material such as, but not limited to,copper or aluminum, and insulator materials such as, but not limited to,dielectric coatings, Nomex™ or other sheet insulators, or hard anodizedsurface treatment for aluminum conductors. Conductor layers may bemanufactured with high speed and low cost manufacturing processes suchas, but not limited to, laser cutting, stamping or fine blanking.Instead of winding conductor wires around posts, the conductor circuitsmay be stamped and then assembled in layers. If insulator layers areused alternately with each conductor layer, the conductor layers may, insome configurations, be assembled without insulation coating.Alternately, conductor circuit layers can be coated with insulationbefore assembly for additional insulation effectiveness, or to eliminatethe need for separate insulating layers.

Non-electrically conductive (or insulated electrically conductive)materials may be used on the same strata as the conductive layers toprovide structural integrity and heat sink/dissipation qualities.Non-filled layers in the slots between conductor layers, or partiallyfilled layers in slots between conductor layers (formed by conductorsthat are narrow enough to create an unfilled gap for the radial lengthof a slot) can also be used to provide a flow path for a cooling gas orliquid so that the open or partially open slots on a layer formconduits. Cooling fluid may also be used as an air or liquid bearingmedium to prevent contact of rotors and stators. Many differentmaterials may be used for spacer layers including, but not limited toanodized aluminum, Torlon™ (a reaction product of trimellitic anhydrideand aromatic diamines), phenolic, or a composite material such as, butnot limited to a metal matrix composite.

Each conductor may be a layer. Layers may be made up of one or moresections. A section can be, for example, a complete circumference of arotary motor, or two or more angular sections of a rotary motor. Eachlayer in each section may be a conductor circuit for only one phase. Ina common electrical machine with wire windings, the conductor wire ishelically wound and overlaps other wire in that phase and/or wire fromother phases. This type of 3-dimensional wire winding configurationcannot be fabricated with a single layer per phase because a simplelayered assembly does not allow the interwoven or helically overlappingconstruction that typical post winding requires.

A bendable wire may be used to create a poly-phase motor with eachadjacent slot comprising conductors from a different phase or differentcombination of phases than an adjacent slot. This has a number ofadvantages which include simplified manufacturing for reduced cost andthe ability to provide very effective cooling as described below.

The conductor manufacturing methods disclosed are especially effectivein constructing devices with high pole density, as they eliminate thehigh precision wire winding mechanisms that otherwise may be needed atthese high slot densities.

A single layer per phase winding in an embodiment may provide aconductor in two adjacent slots and then skipping one or more slots(depending on the number of phases, for example) such that a layerexists in two adjacent slots followed by one or more slots with noconductors on that layer from that phase. Thus, in an electric machinewhere electromagnetic elements of a carrier comprise posts, with slotsbetween the posts, one or more slots are without an electric conductorat a level in the one or more slots corresponding to a location of anelectric conductor in an adjacent slot.

In some embodiments, the disclosed electric machine not only provides ahigh cross sectional area for fluid flow, it provides a consistentlydistributed airflow channel pattern from the inward facing end of theslot to the outward facing end of a slot which ensures that a highpercentage of conductors are in contact with the cooling fluid includingup to every conductor being in contact with the cooling fluid in eachslot. In other words, in an embodiment, there are never more than twolayers of conductor layers contacting at a time. The sequence verticallyin a slot may be for exampleconductor-conductor-space-conductor-conductor-space-conductor-conductor-space.This means that one side of all conductors is always in contact with thefluid in the cooling channels that is created by the missing conductor.This evenly distributed cooling channel array assists in achievingsufficient heat dissipation to compensate for the higher heat productionthat results from the reduced conductor volume due to shorter posts.

Some embodiments of a cooling channel spacing pattern include overlap ofpart but not all of the end turns of a conductor combined with offset ofthe phases combined with a gap at the end of each of the posts to allowtangential and then radial airflow at the end of each post beforeexiting a fluid flow passage between and around the conductors. Withthese details, the airgaps can be consistently spaced, fewer (larger)channels can be avoided, the conductor surface area exposed to thecooling fluid can be increased and there are no stagnant fluid gaps dueto no post-end tangential conduit. Testing has shown that variations ofthis geometry allow effective enough cooling to allow air flow to besufficient to maintain acceptable conductor temperatures at currentdensities that would require liquid cooling with common coolingstrategies such as water cooling of a common motor housing.

In an embodiment, there may be two slots in a row with a conductor froma phase followed by p minus 2 slots with no conductor from any phase onthat layer (with p being the number of phases). For three phases thatwould be two slots with a conductor from a phase followed by one slotwith no conductor from that, or any other, phase. With four phases itwould be two slots in a row with a conductor from a phase followed bytwo slots with no conductor from that, or any other phase on that layer,and so on. No conductor from that or any other phase means there is anair space or a space that can be filled with potting compound and/or afiller material such as a heat extracting insert, or that the space canbe used to route a moving cooling fluid such as gas or liquid

With a three phase configuration, as a non-limiting example, twoadjacent slots will have a single layer with a conductor from a firstphase in a first and second slot followed by a third slot which will nothave a conductor on that layer. This pattern repeats to provide a singlelayer of winding to provide a conductor from a single phase on bothcircumferential sides for every first of three posts on that layer. Onanother layer, a second phase circuit exists on a single layer and has aconductor from this second phase in the second and third slot followedby a slot that will not have a conductor from any phase on that layer. Athird phase is on another separate layer with conductors in every thirdand first slot but no conductor from any layer in every second slot. Inthis three phase configuration, each phase circuit defines a selectionof slots in which, in sets of three slots, two of each set of threeslots receive conductors. In other phase configurations differentselections of slots may be used. Each conductor layer may then receive asingle phase of electrical excitation.

A layered construction permits scalable construction. Layeredconstruction allows components to be deposited with additivemanufacturing processes, or to be assembled with each conductor and/orinsulator component and/or spacer layer being pre-fabricated from asingle or multiple parts.

This conductor configuration may be done with a bendable wire conductoron each layer (which is only helically wound on two posts at the ends ofeach section to connect to the next layer, for a non-limiting example).Or this conductor configuration can be assembled from pre-fabricatedconductor layers so that little or no bending of the conductors isrequired during construction and assembly.

Skipping a conductor in periodic slots can be used as a cooling channelsto allow direct cooling of a high percentage of the surface area of theconductors and/or insulating layers and/or EM posts. The skipping ofconductors in slots may occur in plural slots per layer, spacedperiodically. The cooling channel or conduit may be provided with a flowof coolant. In some embodiments, the cooling channel or conduit may beconnected to a source of cooling fluid. The missing conductor inperiodic slots can be used as an air or other gas flow cooling channelso as to reduce the weight of the device as compared to using a higherdensity fluid such as water or oil at an artificially low temperaturefor increased efficiency in certain applications. Conduits maycommunicate axially to orifices for exhausting coolant flow.

Disclosed embodiments with conductor layers may be assembled by hand ormachine, and then may be clamped between two flat surfaces and pottedwith a potting compound. During the potting process, the top and bottommold plates can be retracted enough to allow wetting of all surfacesbefore being brought axially together again into contact or closeproximity. The lengths of the posts may be used to position the upperand lower potting mold parts (not shown).

If internal cooling is desired, the potting compound is removed from theopen slot sections such as by allowing gravity to remove pottingcompound from the large gaps, or by pushing air through the device topush the potting compound out of the cavities, or by spinning the statorto remove potting compound from coolant channels with centrifugal force.Airflow or centrifugal force, in this operation, may be low enough thatit does not remove potting compound from between close fittingcomponents.

Layers can be bonded together or fused together or otherwise fastenedtogether. If some internal layers, such as but not limited to the copperlayers and spacer layers between the anodized aluminum or otherseparator layers, are tinned, and if all components or their coatingsare bondable by a given solder compound, the parts can be assembled andthen heated under pressure in an oven to fuse everything together. It isimportant, if pre-tinning with solder is used, that the separationlayers are coated with a suitable insulator such as hard anodizing sothere is no conductor layer-to-layer conductivity. Alternatively, athermoplastic resin can be used to coat the parts and they can then beassembled and heated and fused in an oven under enough pressure toensure the correct axial and other dimensions. An epoxy or otherhardening adhesive can be used during or after assembly to adhere andpot the components. If airflow channels are included in the design,potting can be followed by blowing or spinning the adhesive out of thelarge chambers before the epoxy hardens. An advantage of a pre-preg orsolder tinning process which provides a thin and consistent coat ofadhesive or solder, is that the airflow channels may not need to bepurged. Only the close fitting surfaces will adhere to each other. Anynumber of posts or permanent magnets may be used. Using solder as abonding agent will also provide excellent heat transfer from theconductors to hard anodized insulating layers and to the cooling fluidin the cooling channels.

An exemplary embodiment may be configured with multiple layers ofstators and/or PM carriers with PM carriers on both axial ends of one ormore stators or two or more stators on the axial ends of one or more PMcarriers. Only the stator and/or PM carrier at the axial ends may have abackiron.

In embodiments of layered conductors, the cross sectional area of theend turns may be greater than the average or maximum cross sectionalarea of the conductors in the slots. This reduces the resistance in theend turns allowing them to run cooler than the slot portion of theconductors and to therefore act as effective heat sinks for theconductors in the slots and to increase the heat capacity of theconductors to increase the ability to operate at very high currentdensities for short periods of times such as during emergency stops oreven during normal operation during high accelerations. The end turnsmay be wider than the slot turns. The end turns may also have uniformwidth. Furthermore, the greater surface area of the end turns ascompared to the slot portions of the conductors provides a cooling fineffect that is highly effective due to the low heat flow resistance fromthe slot turns to the end turns as a result of them being of the samecomponent and of a high thermal conductivity material such as copper oraluminum. Cooling these end turn “cooling fins” can be done with anynumber of liquid or gas cooling means, with or without theabovementioned slot channel cooling.

The above can be configured with two or more stators on either axial endof one or more PM carriers. PM carrier can have any type of PM magnetand can be configured with a Halbach array or pseudo Halbach array (withPMs polarized in the direction of carrier motion with steel between themto provide flux linkage). The stator and “rotor” may both be energizedto reduce or eliminate the need for permanent magnets. Any number orgeometry or size of posts and PMs or other components may be used.Manufacturing techniques include PCB manufacturing techniques withconductive traces used for coils and posts assembled with pick-and-placeequipment. Larger motors or actuators or generators can use apre-fabricated conductor process as described for other embodiments inthis disclosure.

In some embodiments of an electric machine, windings are provided insingle layers, either interdigitated with windings of adjacent posts orside by side. Single layers provide reduced wire length produces lessheat for a given current. Direct contact of all wires (through theinsulation) provides a lower heat flow resistance path for the heat todissipate from the wires to the housing or other cooling members.Shorter posts shorten the path for the heat from the wires to thehousing. Increased post number can increase the surface area of thestator (or rotor) which can provide greater surface area on the statorto act as radiant or convective cooling fins for the heat produced inthe stator (or rotor) and coils. These features contribute to theability to run higher current through the conductors than wouldotherwise be the case.

Various design features may be used in any of the embodiments disclosed.Slot fill may be as high as possible, and with short posts relative todiameter the slot walls are more parallel, making slot fill higher.Current density depends on the materials used, but may be increased dueto the enhanced cooling effect of the disclosed geometry. The disclosedgeometry may be used with any suitable number of phases such as 3 or 5.Concentrated or distributed windings may be used. Various post shapesmay be used, for example parallel sides. Stator pole to rotor pole ratiomay be 5:4, for example 5 posts for each 4 permanent magnets. However,various ratios may be used. Active cooling may also be used. The airgapmay be for example 0.005″ to 0.009″ but smaller airgaps may be used, atsome risk of manufacturing complexity, or larger, at some loss oftorque. Magnet dimensions may be 1:1 circumferential width to radialheight but other dimensions may be used. In calculating weight of amotor for the analyses presented, the weight is the stator backironthickness plus post height plus copper volume plus PM volume plus rotorbackiron. Various forced cooling methods may be used, although thedisclosed analyses assume a fluid cooled housing.

The disclosed pole density and conductor volume (post height)characteristics may be applied to all types of electric machines withslots and teeth including the following electric machines: DC, AC,synchronous, asynchronous, axial, radial, inner stator, outer stator,linear, induction, brushless, PM, switched reluctance, doubly-salient,flux-reversal, flux-switching, hybrid-excited, flux mnemonic,magnetic-geared, vernier, magnetless, doubly-fed Vernier and doublerotor.

With increasing output torque, magnetic forces can cause distortion ofthe stator and/or rotor, resulting a lack of precision, increased noise,vibration, fatigue stress and eventually failure of the components. Amore even distribution of magnetic forces may be provided through thedisclosed pole density, post-to-PM ratio, and conductor windings thatprovide that the majority of adjacent stator posts are energized bydifferent phases. In an embodiment, a combination of these featurescauses magnetic forces to repeat on average every three posts. This, incombination with the very high pole density, results in a very evendistribution of forces on the stator and rotor which, in someembodiments, reduces manufacturing cost and complexity and eliminatesthe need for additional bearings and support structure.

In some embodiments there is a reduced rigidity requirement by coatingthe airgap with a low friction surface that maintains the airgap. In anembodiment of a linear motor a low friction surface is applied in theairgap which maintains a 0.008″ airgap. Coatings, such as DLC(diamond-like coating), can be deposited at 0.0025″ on both the rotorand the stator and the gap will be maintained.

Equations Defining Pole Density and Post Height

Ranges of pole pitch (or density) and conductor volume have been foundwhich give a significant benefit either in terms of KR, or in terms of aweighting function combining torque, torque-to-weight, and Km (asdescribed further). The amount of benefit in terms of the weightingfunction is dependent on the amount of cooling and other factors, butthe equations define novel structures of electric machines that providebenefits as indicated. Equations are given which define bounded regionsdetermined by the ranges of pole density and conductor volume whichyield these benefits.

In an embodiment, advantages are obtained by operating within a regionof a phase space defined by machine size, pole density and post height.A series of graphs shown in FIG. 170A to FIG. 170F, show torque density(z axis) v slot density (x axis) and post height (y axis) for anexemplary series of linear motor section geometries, created andanalysed using FEMM software using an automated solver generated inOCTAVE™ (which is a program for solving numerical computations). Slotdensity was used in this example because it is the same as pole density.

The following rules and assumptions were applied to all of the motors inthe series. Each section consisted of 144 electromagnets and 146permanent magnets. The rotor comprised sections of NdFeB 52 magnets andM-19 silicon steel. Every permanent magnet was placed tangentially tothe rotor and oriented so that its magnetic field direction was alignedtangentially to the rotor and are opposite to its adjacent permanentmagnets. M-19 silicon steel sections were placed between permanentmagnets. The stator was made from M-19 silicon steel. The electromagnetsused concentrated winding coils in a 3-phase configuration. A 75% fillfactor of the coils was assumed, consisting of 75% of the slot area. Thetwo variables that were investigated were the post height and slotdensity. The remainder of the geometry variables were scaled accordingto the following relationships: 1.25 inches constant model thicknessacross all simulations, Rotor permanent magnet width is set at 50% ofpermanent magnet pitch, Rotor permanent magnet height is set at 2.3times of permanent magnet width, Stator slot width is 50% of statorelectromagnet pitch (equal width of posts and slots), Stator back ironheight is set at 50% of stator post width, Airgap axial height of 0.005inches.

The bounded region which represents the unique geometry disclosed ismodeled for the preferred embodiment, namely the embodiment which willyield the highest torque-to-weight and KR. Certain design choices havebeen made in this embodiment such as the selection of grade N52 NdFeBmagnets in the rotor, a rotor pole to stator post ratio of 146:144, anda flux concentrating rotor with back iron. To the best of the inventor'sknowledge, this configuration represents one of the highest practicaltorque-to-weight configurations for sizes of actuators in the discloseddiameters while still retaining a reasonable level of manufacturabilityand structural stability. Many other configurations are possible such asdifferent rotor types (surface permanent magnet, buried permanentmagnet, etc), different magnet materials and grades including but notlimited to ceramic, samarium cobalt, and high-temperature NdFeB,different rotor pole to stator post ratios, different stator windingconfigurations, different stator materials, etc. In many cases,different design choices for these parameters will not have as great aKR benefit as compared to the preferred embodiment by either resultingin reduced torque or increased weight for the same pole pitch and postheight as the preferred embodiment. However, for the majority ofdesigns, there is a benefit to KR by using the pole pitch and postheight of inside the disclosed region over geometry outside thedisclosed region when all other design variables and geometricalrelationships are held constant. This principle holds true for bothconcentrated and distributed winding designs, for linear motors, axialflux rotary motors, radial flux rotary motors, trapezoidal/toroidalrotary motors, and transverse flux linear and rotary motors.

For each of those motor section geometries, magnetic simulation and heatsimulation were performed. For every magnetic simulation, the programyielded values for mass, horizontal force, and power consumption.Geometrical extrapolations of the coil cross sections were used to findthe mass and power consumption of the end windings in order to moreaccurately predict the mass and power consumption of the entire system.For calculating stall torque and torque at low speed, the square root ofresistive losses is the dominant part of the power consumption, with amultiplier based on the slot geometry to account for the resistivelosses of the end windings. These values were used to calculate the massforce density (force per unit mass) and the area-normalized force (forceper unit area of the airgap) of each simulation. For every heatsimulation, the program yielded values for coil temperature, rotortemperature and stator temperature. A set cooling rate was applied tothe stator inner surface using water as the coolant and a convectioncoefficient of 700 W/m²K. The temperature of the water was set at 15° C.and it had a flow rate between 6-20 mm/s. Steady state conditions wereassumed.

For constant current density simulations, a fixed current density wasapplied to the conductor and the resulting force, mass, powerconsumption, and maximum stator temperature were calculated by theprogram.

For constant temperature, force per area, or force density simulations,the current density was adjusted at each geometry point until theparameter of interest reached the target value, and the other parameterswere recorded at that point. The target error for constant temperature,force per area, and force density simulations are 1 degrees, 0.002N/mm², and 1 N/kg respectively. This data can be directly applied to anysize of rotary motor by multiplying the area-normalized force by thecircumferential area of the airgap in the rotary motor, and multiplyingthe force by the diameter to yield the resulting torque. There will besome small deviations due to the radius of curvature of the motor, andthe errors associated with approximating a curved structure with alinear one, however our simulations have shown the rotary simulatedtorque typically to be within 10% of that predicted by the linear model.

High torque-to-weight is of benefit in some applications, but a minimumlevel of torque may be necessary for applications such as robotics wherethe arm, no matter how light it may be as a result of hightorque-to-weight actuators, must still have enough torque to lift andmove a payload. Electric machines having a pole density and conductorvolume within the ranges disclosed in this patent document provide hightorque and torque-to-weight at acceptable power consumption levels.

The force per area at a constant current density 2320 is plotted in FIG.170A as a function of slot pitch and post height. The same currentapplied to all motors in the virtual series results in dramaticallylower force per area in the disclosed ranges 2322 (indicatedschematically by the dashed lines). The dashed lines correspond to themiddle boundary from each size (25 mm, 50 m, 100 mm and 200 mm asdiscussed in relation to the equations below) projected onto the 3Dsurface. The middle boundaries correspond to the sets of equations A2,B2, C2 and D2. In this graph, the force per area at constant currentdensity 2320 is shown for a series of motors that were analyzed in FEMMusing a script in OCTAVE to find the highest torque rotary position fora given 3 phase input power. These motors are identical in every wayapart from the conductor volume and slot density, which are varied asshown.

Surprising effect of constant temperature current density. The highestcurrent density possible at a given temperature 2324 is plotted in FIG.170B as a function of slot pitch and post height. The exponentiallyhigher heat dissipation characteristic in the disclosed ranges 2322allows much higher current density at a given temperature. Low conductorvolume tends to reduce the actuator weight, but low conductor volumealso tends to reduce the actuator torque. When the conductor volume andslot density is in the disclosed ranges, however, there is a dramaticreduction in the heat flow resistance from the conductors to the back ofthe stator or to any other surface where cooling can be applied, thusallowing very high current densities to be applied to the conductorswithout overheating the actuator.

In FIG. 170B, the same series of motors is used as in FIG. 170A, butinstead of constant current density applied to each motor, the currentdensity was varied until the steady state temperature of the conductorswas ˜70° C. A reasonable representation of a typical water coolingeffect was applied to the outer axial surface of the stators at aconvection coefficient of 700 W/m²K. The temperature of the water wasset at 15° C. Ambient temperature was set at 15° C. No air convectivecooling was applied to the rotor for simplicity because the water cooledsurface was highly dominant in terms of cooling and because the rotorwas not producing heat of its own. Steady state conditions were assumed.For each point on the 3D graph, the current density of the motor wasincreased from zero until the temperature of the coils reached ˜70 degC.

FIG. 170C is the same as FIG. 170D except that it has constant currentat 6 A/mm2 as apposed to constant temperature of 70 deg C. Thusdemonstrating how the heat dissipation benefit of short posts giveunexpected benefit disclosed range FIG. 170C was developed using thefollowing weighting convention, Torque—weighting of 1,Torque-to-weight—weighting of 3, Power consumption—weighting of 2.Torque-to-weight was the most highly weighted because the weight of thearm is determined by the weight of the actuator and because the weightof the arm will typically be significantly higher than the weight of thepayload. Torque was weighted at 1 to include it as an importantconsideration but recognizing that the payload may be quite a bit lowerthan the weight of the arm. Power consumption was given a moderateweighting because it is an important consideration, but powerconsumption is known to benefit from lower arm weight, as isaccomplished by a higher weighting on torque-to-weight, so a higherweighting on power consumption was deemed to be potentiallycounter-productive.

By applying a constant current density to the series of motors, andcombining the results with the above weighting, the surface 2328 in FIG.170D shows a trend toward lower overall performance toward andcontinuing through the disclosed ranges 2322 of slot (or pole) densityand conductor volume. FIG. 170D shows a benefit in the disclosed rangewhen the constant temperature current density is applied from FIG. 170B.

FIG. 170E KM—An industry standard metric for motor capability is the KMwhich is basically torque-to-power consumption. KM assumes sufficientcooling for a given electrical power. It only considers the amount ofpower required to produce a certain level of torque. The K_(m)″ surface2330 as a function of slot pitch and post height is plotted in FIG.170E.

FIG. 170F K_(R)″. The torque to weight to power consumption shows themost unexpected and dramatic benefit in the disclosed ranges 2322 asseen from the graph of the K_(R)″ surface 2332 as a function of slotpitch and post height in FIG. 170F. High K_(R) may not be of greatbenefit in stationary applications, but in applications such asrobotics, K_(R) indicates that power consumption benefits can beachieved by reducing the weight of the entire system.

A method of producing a graph showing how K_(R)″ varies with poledensity and post height is as follows. Consider a motor section withgeometry A having low conductor volume (low post height) and low poledensity. The motor section with geometry A is simulated; a set coolingrate is applied to the stator inner surface using water as the coolantand a convection coefficient of 700 W/m²K. The temperature of the wateris set at 15° C. and it has a flow rate between 6-20 mm/s. Steady stateconditions are assumed. The current passing through the conductor ofgeometry A is then increased until the maximum temperature of theconductors reaches 70° C. The torque density of geometry A at this pointis then recorded and plotted in the graph for the corresponding valuesof post height and pole density. The process is repeated for othergeometries, obtained, by example, through varying the post height andpole density and scaling the remaining parameters as described above.For instance, a geometry B may be is obtained from geometry A byincreasing the post height, with all other parameters scaled asdescribed above. A geometry C may have the same post height as geometryA but greater pole density. A geometry D may have increased post heightand increased pole density as compared to geometry A. Plotting thetorque densities results in a surface in a graph.

It is found that the torque density increases as pole density increasesand post height decreases. No such increase in torque density is shownto occur with geometries having either a low post height or a high poledensity; the benefit in torque density is only observed for geometriescombining these two factors. Yet, in this region, efficiency isdecreasing. While the graph was produced based on the assumptionsindicated, the inventor soundly predicts, based on the disclosed coolingeffect and reduction of flux losses of increasing pole density anddecreasing conductor volume or post height, that the same geometry willhave a benefit at other values of the parameters that were used in thesimulations. Changes in motor design elements which do not affect postheight or pole density are not expected to result in a loss of thebenefits. For instance, an electric machine comprising a rotor withtangentially oriented permanent magnets and an analogous electricmachine comprising a rotor with surface-mounted permanent magnets maypossess somewhat different K_(R)″ surfaces; nonetheless, the principlesdescribed above will still apply and a benefit would still be predictedwithin the region of geometries of low post height and high pole densitydescribed previously. As currently understood, the principles apply onlyto electric machines with posts, such as axial flux and radial fluxmachines.

In the disclosed equations and graphs, the parameter K_(R)″ issize-independent and has been converted from a conventional K_(R) to useforce instead of torque, and to be independent of both circumferentiallength and axial length. Therefore, the conventional K_(R) of any sizemotor can be found from the K_(R)″ value. And for two motors ofidentical size (diameter at the airgap and axial length) but differentgeometry (i.e. pole density and/or post height), the multiplying factorwill be the same, so the motor with higher K_(R)″ will have a higherconventional K_(R).

K_(R)″ as a function of pole density and post height greatly resemblesthe surface of a graph showing conventional KR. However, this particularsurface, corresponding to the torque density, may change considerablywhen different temperatures are used as the constraint in the analysis.K_(R)″, by contrast, does not change substantially (provided the currentdoesn't get sufficiently high for the motors in the series start tosaturate; then the 3D curve shape will change.) It is the K_(R)″,therefore, that is used to define the specific range of pole density andpost height which result in the previously-discussed benefits.

The ranges of benefit disclosed depend on the resultant motor diameterat the airgap. Smaller motors are more constrained because the physicalsize of the motor prevents lower slot densities from being used. We havedefined 4 discrete motor diameter ranges corresponding to 200 mm andabove, 100 mm and above, 50 mm and above, and 25 mm and above. For eachdiameter range, we describe three levels of K_(R)″. The firstcorresponds to where a small benefit to K_(R)″ begins, the second to amoderate K_(R)″ benefit, and the third to a high K_(R)″ benefit for thatspecific diameter range. Higher K_(R)″ values generally correspond tolower overall torque values for that motor size range.

These motor sizes disclosed (25 mm and up to 200 mm diameter and above)represent small to large motors. The airgap of 0.005 inches used in thesimulation is believed to be the smallest reasonable airgap size forthis range of motors. Smaller airgaps are not practical for this motorrange due to manufacturing tolerances, bearing precision, componentdeflection, and thermal expansion.

The coefficients in the equations above were chosen in a manner to boundthe region of interest and make the resulting relation nearlycontinuous.

A 50:50 ratio of post:slot width was chosen for these simulations, asanalysis had shown that highest benefits are obtained when the ratio isbetween 40:60 and 60:40. A 50:50 ratio represents a typical best-casescenario; at fixed post height, using a 10:90 slot:post width ratio willhave a significantly degraded performance by comparison. Analysis showsthat at constant post height, an embodiment exhibits the maximum oftorque and torque density at a 50% slot width, and the maximum of Km andKr at 40% slot width. However, the maximum values of Km and Kr arewithin 5% of the values given at a 50:50 geometry; consequently a 50:50ratio was viewed as a reasonable choice of scaling parameter for thesimulations. Other ratios of post:slot width would give a portion of thebenefits disclosed.

Equations and graphs are discussed below which show the ranges of poledensity and conductor volume which give a significant benefit either interms of KR, or in terms of a weighting function combining torque,torque-to-weight, and Km, for different embodiments. As with thepreviously-described equations, the region of benefit in terms of theweighting function is dependent on the amount of cooling.

Size of an electric machine means the airgap diameter of an axial fluxmachine or radial flux machine as defined herein or the length in thedirection of translation of the carriers of a linear machine.

The first bounded region corresponds to regions where a significantK_(R) benefit is found with respect to the rest of the geometries in thedomain. For a given device size, K_(R) has a higher value in thedisclosed range of geometry than anywhere outside of the range,indicating potential benefits to overall system efficiency for certainapplications using devices of these geometries. The graph of K_(R)″ isused to define the boundary by placing a horizontal plane through at aspecified K_(R)″ value. Four values of K_(R)″ are used to define areasof benefit for four different actuator size ranges corresponding tosizes of 200 mm and larger, 100 mm and larger, 50 mm and larger, and 25mm and larger.

In the following tables, pole pitch is represented by the variable S, inmm. Post height is also represented in millimetres.

In a machine with 25 mm size, the boundary line for K_(R)″>3.3 isdefined by the values shown in Table 1 and the corresponding graph isFIG. 180.

TABLE 1 Set A1 Points Post Height > Pole Pitch Post Height −1.070 * S +2.002  for 0.572 < S < 1.189 0.572 1.390  1.175 * S + −0.667 for 1.189 <S < 2.269 1.189 0.730 13.502 * S − 28.637 for 2.269 < S < 2.500 2.2691.999 Post Height < 2.500 5.118 −5.898 * S + 19.863 for 1.970 < S <2.500 1.970 8.244 0.229 * S + 7.794 for 1.349 < S < 1.970 1.349 8.1027.607 * S − 2.160 for 0.723 < S < 1.349 0.723 3.340 11.430 * S − 4.924 for 0.572 < S < 0.723 0.572 1.614 0.572 1.390

In a machine with 25 mm size, the boundary line for K_(R)″>3.4 isdefined by the values shown in Table 2 and the corresponding graph isFIG. 181.

TABLE 2 Set A2 Points Post Post Height > Pole Pitch Height −1.340 * S +2.305  for 0.619 < S < 1.120 0.619 1.475 1.100 * S − 0.429 for 1.120 < S< 2.074 1.120 0.803 3.830 * S − 6.082 for 2.074 < S < 2.269 2.074 1.852Post Height < 2.269 2.598 −69.510 * S + 160.318 for 2.222 < S < 2.2692.222 5.865 −3.430 * S + 13.492 for 1.667 < S < 2.222 1.667 7.7702.830 * S + 3.056 for 1.133 < S < 1.667 1.133 6.260 8.650 * S − 3.545for 0.619 < S < 1.133 0.619 1.812 0.619 1.475

In a machine with 25 mm size, the boundary line for K_(R)″>3.6 isdefined by the values shown in Table 3 and the corresponding graph isFIG. 182.

TABLE 3 Set A3 Points Post Post Height > Pole Pitch Height −4.160 * S +5.032  for 0.723 < S < 0.967 0.723 2.024 0.839 * S + 0.198 for 0.967 < S< 1.692 0.967 1.009 2.713 * S − 2.973 for 1.692 < S < 1.939 1.692 1.617Post Height < 1.939 2.287 −53.233 * S + 105.506 for 1.879 < S < 1.9391.879 5.481 −1.406 * S + 8.122  for 1.465 < S < 1.879 1.465 6.0633.898 * S + 0.353 for 1.035 < S < 1.465 1.035 4.387 7.535 * S − 3.412for 0.723 < S < 1.035 0.723 2.036 0.723 2.024

In a machine with 50 mm size, the boundary line for K_(R)″>2.2 isdefined by the values in Table 4 and the corresponding graph is FIG.177.

TABLE 4 Set B1 Points Post Post Height > Pole Pitch Height 0.254 * S +0.462 for 0.319 < S < 3.667 0.319 0.543  2.665 * S + −8.380 for 3.667 <S < 5.000 3.667 1.394 5.000 4.947 Post Height < 4.500 14.088 −18.282 *S + 96.357  for 4.500 < S < 5.000 2.738 22.304 −4.663 * S + 35.071 for2.738 < S < 4.500 1.447 18.967  2.585 * S + 15.227 for 1.447 < S < 2.7380.319 0.904 16.013 * S − 4.204  for 0.319 < S < 1.447 0.319 0.543

In a machine with 50 mm size, the boundary line for K_(R)″>2.5 isdefined by the values in Table 5, and the corresponding graph is FIG.178.

TABLE 5 Set B2 Points Post Post Height > Pole Pitch Height 0.269 * S +0.456 for 0.380 < S < 3.016 0.380 0.558 3.051 * S − 7.936 for 3.016 < S< 4.167 3.016 1.267 Post Height < 4.167 4.779 −14.766 * S + 66.309  for3.667 < S < 4.167 3.667 12.162 −3.952 * S + 26.654 for 2.315 < S < 3.6672.315 17.505  3.108 * S + 10.310 for 1.278 < S < 2.315 1.278 14.28214.542 * S − 4.303  for 0.389 < S < 1.278 0.389 1.354 88.444 * S −33.051 for 0.380 < S < 0.389 0.380 0.558

In a machine with 50 mm size, the boundary line for K_(R)″>2.9 isdefined by the values in Table 6, and the corresponding graph is FIG.179.

TABLE 6 Set B3 Points Post Post Height > Pole Pitch Height 0.191 * S +0.626 for 0.472 < S < 2.181 0.472 0.716 2.135 * S − 3.613 for 2.181 < S< 3.095 2.181 1.043  53.475 * S − 162.511 for 3.095 < S < 3.175 3.0952.994 Post Height < 3.175 7.272 −5.095 * S + 23.450 for 2.222 < S <3.175 2.222 12.128  0.805 * S + 10.339 for 1.381 < S < 2.222 1.38111.451 10.251 * S − 2.706  for 0.572 < S < 1.381 0.572 3.158 24.420 * S− 10.810 for 0.472 < S < 0.572 0.472 0.716

In a machine with 100 mm size, the boundary line for K_(R)″>1.5 isdefined by the values in Table 7, and the corresponding graph is FIG.174.

TABLE 7 Set C1 Points Post Post Height > Pole Pitch Height 0.322 * S +0.359 for 0.233 < S < 6.667 0.233 0.434  2.202 * S − 12.179 for 6.667 <S < 8.333 6.667 2.504 Post Height < 8.333 6.173 −25.555 * S + 219.122for 7.778 < S < 8.333 7.778 20.356 −5.585 * S + 63.794 for 4.000 < S <7.778 4.000 41.455  3.214 * S + 28.600 for 1.793 < S < 4.000 1.79334.362 21.749 * S − 4.633  for 0.233 < S < 1.793 0.233 0.434

In a machine with 100 mm size, the boundary line for K_(R)″>1.7 isdefined by the values in Table 8, and the corresponding graph is FIG.175.

TABLE 8 Set C2 Points Pole Post Pitch Height    Post Height> 0.277*S +0.593 for 0.250 < S < 5.182 0.250 0.662  2.342*S − 10.111 for 5.182 < S< 7.222 5.182 2.026    Post Height< 7.222 6.804 −13.149*S + 101.763 for6.111 < S < 7.222 6.111 21.412 −4.885*S + 51.265 for 3.333 < S < 6.1113.333 34.983  4.291*S + 20.680 for 1.520 < S < 3.333 1.520 27.20320.788*S − 4.395  for 0.251 < S < 1.520 0.251 0.823 161.000*S − 39.588 for 0.250 < S < 0.251 0.250 0.662

In a machine with 100 mm size, the boundary line for K_(R)″>1.9 isdefined by the values in Table 9, and the corresponding graph is FIG.176.

TABLE 9 Set C3 Points Pole Post Pitch Height    Post Height> 0.277*S +0.591 for 0.278 < S < 4.425 0.278 0.668 1.916*S − 6.663 for 4.425 < S <6.111 4.425 1.817    Post Height< 6.111 5.048 −21.337*S + 135.438 for5.556 < S < 6.111 5.556 16.890 −4.985*S + 44.588 for 3.175 < S < 5.5563.175 28.76  2.749*S + 20.031 for 1.560 < S < 3.175 1.560 24.32018.321*S − 4.260  for 0.278 < S < 1.560 0.278 0.833 0.278 0.646

In a machine with 200 mm size, the boundary line for K_(R)″>1.3 isdefined by the values in Table 10, and the corresponding graph is FIG.171.

TABLE 10 Set D1 Points Pole Post Pitch Height     Post Height> 0.257*S + 0.327 for 0.208 < S < 7.778 0.208 0.381  1.977 *S + −13.044 for7.778 < S < 9.444 7.778 2.330     Post Height< 9.444 5.623 −36.195 *S +347.445  for 8.889 < S < 9.444 8.889 25.711 −5.777 *S + 77.062  for4.833 < S < 8.889 4.833 49.142  1.950 *S + 39.718 for 2.222 < S < 4.8332.222 44.051 20.301 *S + −1.058 for 0.389 < S < 2.222 0.389 6.839 34.481*S + −6.574 0.208 < S < 0.389 0.208 0.598 0.208 0.381

In a machine with 200 mm size, the boundary line for K_(R)″>1.5 isdefined by the values in Table 11, and the corresponding graph is FIG.172.

TABLE 11 Set D2 Points Pole Post Pitch Height     Post Height> 0.322*S + 0.359 for 0.233 < S < 6.667 0.233 0.434   2.202 *S + −12.179 for6.667 < S < 8.333 6.667 2.504     Post Height< 8.333 6.173 −25.555 *S +219.122 for 7.778 < S < 8.333 7.778 20.356 −5.585 *S + 63.794 for 4.000< S < 7.778 4.000 41.455  3.214 *S + 28.600 for 1.793 < S < 4.000 1.79334.362  21.749 *S + −4.633 for 0.233 < S < 1.793 0.233 0.434

In a machine with 200 mm size, the boundary line for K_(R)″>1.8 isdefined by the values in Table 12, and the corresponding graph is FIG.173.

TABLE 12 Set D3 Points Pole Post Pitch Height Post Height> 0.212 *S +0.600    for 0.264 < S < 4.833 0.264 0.656 3.017 *S + −12.960    for4.833 < S < 6.667 4.833 1.623 Post Height< 6.667 7.157 −12.356 *S +89.531     for 5.556 < S < 6.667 5.556 20.884 −4.551 *S + 46.170     for3.175 < S < 5.556 3.175 31.72 3.850 *S + 19.496    for 1.502 < S < 3.1751.502 25.279 19.751 *S + −4.387     for 0.264 < S < 1.502 0.264 0.8270.264 0.656

At each machine size, each boundary line is defined for a given K″value, such that for each machine size there is a set of K″ values and acorresponding set of boundary lines. Pairs of boundary lines can bechosen, in which one boundary line is chosen from each of twoconsecutive sizes of device, i.e. 25 mm and 50 mm, 50 mm and 100 mm, or100 mm and 200 mm. The boundary lines occupy a space or volume definedby size, pole pitch and post height. A boundary surface may be definedas the two-dimensional uninterrupted surface in the space that is theexterior surface of the union of all lines that connect an arbitrarypoint in the first boundary line and an arbitrary point in the secondboundary line. The boundary surface encloses a benefit space. For eachpair of boundary lines, the boundary surface defines a benefit space. Anelectric machine with a size, pole pitch and post height that is withina given benefit space is considered to fall within the embodimentdefined by the corresponding boundary lines for that size of machine.

For machine sizes greater than the largest calculated size, the boundarylines calculated for the largest calculated size are used. The benefitspace beyond the largest calculated size is thus simply the surfacedefined by the calculated boundary lines for that size and the volume ofpoints corresponding to greater size but with pole pitch and post heightequal to a point on the surface.

The main components of an electric machine comprise a first carrier(rotor, stator, or part of linear machine) having an array ofelectromagnetic elements and a second carrier having electromagneticelements defining magnetic poles, the second carrier being arranged tomove relative to the first carrier for example by bearings, which couldbe magnetic bearings. The movement may be caused by interaction ofmagnetic flux produced by electromagnetic elements of the first carrierand of the second carrier (motor embodiment) or by an external source,in which case the movement causes electromotive force to be produced inwindings of the electric machine (generator embodiment). An airgap isprovided between the first carrier and the second carrier. Theelectromagnetic elements of the first carrier include posts, with slotsbetween the posts, one or more electric conductors in each slot, theposts of the first carrier having a post height in mm. The first carrierand the second carrier together define a size of the electric machine.The magnetic poles having a pole pitch in mm. The size of the motor,pole pitch and post height are selected to fall within a region in aspace defined by size, pole pitch and post height. The region is definedby 1) a union of a) a first surface defined by a first set ofinequalities for a first size of electric machine, b) a second surfacedefined by a second set of inequalities for a second size of electricmachine; and c) a set defined as containing all points lying on linesegments having a first end point on the first surface and a second endpoint on the second surface, or 2) a surface defined by a set ofinequalities and all points corresponding to greater size but with polepitch and post height corresponding to points on the surface.

The first set of inequalities and the second set of inequalities arerespectively sets of inequalities A and B, or B and C, or C and D whereA is selected from the group of sets of inequalities consisting of theequations set forward in Tables 1, 2 and 3 (respectively sets ofequalities A1, A2 and A3), B is selected from the group of sets ofinequalities consisting of the equations set forward in Tables 4, 5 and6 (respectively sets of equalities B1, B2 and B3), C is selected fromthe group of sets of inequalities consisting of the equations setforward in Tables 7, 8 and 9 (respectively sets of inequalities C1, C2,C3) and D is selected from the group of sets of inequalities consistingof the inequalities set forward in Tables 10, 11 and 12 (respectivelysets of inequalities D1, D2 and D3).

The space in which the electric machine is characterized may be formedby any pair of inequalities that are defined by sets of inequalities foradjacent sizes, for example: A1 B1, A1 B2, A1 B3, A2 B1, A2 B2, A2 B3,A3 B1, A3 B2, A3 B3, B1 C1, B1 C2, B1 C3, B2 C1, B2 C2, B2 C3, B3 C1, B3C2, B3 C3, C1 D1, C1 D2, C1 D3, C2 D1, C2 D2, C2 D3, C3 D1, C3 D2, C3D3. It may also be formed by any set of inequalities and all pointscorresponding greater size but having post height and pole pitch withinthe region defined by the set of inequalities.

All of the devices described in this application may have sizes, polepitches and post heights falling within the regions and spaces definedby these equations.

In a simulation of geometry of the embodiment represented by FIG. 1-FIG.5, using a 0.005″ air gap and using N52 magnets, the simulation yields aKR″ of 1.53 Nm/kg/W which is inside of the benefit range for that size.A simulation of the geometry of the embodiment shown in FIG. 128-FIG.129 yielded a KR″ of 2.13 Nm/kg/W which also falls within the benefitrange for that size.

Discussion of Geometry

The range of geometry provides unusually high torque-to-weight for agiven electrical power input. This efficiency is independent oftemperature. For example, at a given torque-to-weight, an actuatorinside the disclosed range, may run cooler, for a given method ofcooling, than a similar actuator outside of the disclosed range, becausedevice device in the disclosed range will use less power.

The low conductor volume, in this case has the benefit of lower thermalresistance due to the shorter conductors. Within the disclosed range,the need to power these conductors at higher current densities is morethan compensated for by the heat dissipation benefits of the device toachieve a given torque-to-weight. Within the disclosed K_(R)″ range, thereduction in weight (which results, in part, from the low conductorvolume) can exceed the extra power required (which results from thehigher current densities) such that net benefit can be produced in termsof KR. The stated ranges of geometry in a machine of the given diameterprovides a heat dissipation effect associated with feature geometryknown for much smaller machines, but used according to the principles ofthe present device, in a large diameter machine.

For clarity, cooling is still needed to achieve the KR benefit, but itis assumed for the K_(R) calculation that adequate cooling is used. Forsome motors and applications, radiative cooling is sufficient. Forothers a fan and cooling fins is needed. For others at full power, watercooling is needed.

For the disclosed electric machine, the K_(R) is the same at low to highpower output (until the stator saturates at which time the K_(R) will bereduced) so different levels of cooling will be needed depending on thepower output but the torque-to-weight-to-power consumption remainsreasonably constant. The disclosed range of pole density and conductorvolume provides unusually high torque-to-weight for a given rate of heatdissipation with a given method of cooling. The disclosed range of poledensity and conductor volume produces higher torque-to-weight for agiven cooling method applied to the back surface of the stator and agiven conductor temperature. The primary form of electrical conductorcooling for the disclosed range of pole density and electrical conductorvolume is thermal conductive heat transfer from the electricalconductors to the back surface of the stator.

Heat can be extracted from the back surface of the stator though directcontact with a cooling fluid or through conduction to another membersuch as a housing, or through radiation, for example. Other surfaces ofthe stator or conductors can also be cooled by various means. Coolingthe back surface of the stator is shown to be a cost effective andsimple option for many motor types. A sample analysis (not shown here)indicates that geometry in the disclosed range which shows better heatdissipation from the back surface of the stator (as compared to motorsoutside of the disclosed range) will also generally show improved heatdissipation than motors outside of the disclosed range when othersurfaces of the stator or conductors are cooled. The back surface of thestator is, therefore, viewed as a useful cooling surface, as well as anindicator of the effectiveness of each motor in the series to theapplication of cooling to other surfaces of the stator and conductors.The back surface of the stator has been chosen for the main coolingsurface for the motor series analysis which is used to identify thedisclosed range.

Other methods of cooling may be applied to an electric machine with thedisclosed range of pole density and conductor volume, but the heat flowpath from conductors to the back of the stator will preferably always beused for cooling the motor regardless of what other types of cooling(EG: direct coil cooling) are used.

Stator Back Iron

Stator back iron may have an axial depth that is 50% of the width(circumferential or tangential width) of the posts. The posts may eachhave a tangential width and the stator may comprise a backiron portion,the backiron portion having a thickness equal to or less than half ofthe tangential width of the posts, or may be less than the tangentialwidth of the posts. Thicker back iron adds weight with minimal benefit.Thinner backiron helps with cooling but the effect of back ironthickness on cooling is not very significant. The backiron surface maybe in physical contact with the housing to conduct heat physically fromthe stator to the housing, and/or the back surface of the stator can beexposed to an actively circulated cooling fluid and/or the back surfaceof the stator can be configured for radiative heat dissipation to theatmosphere or to the housing or other components, and/or the backsurface of the stator can be configured for convective or passivecooling through movement of air or liquid over the surface of the statorand or housing. Gas or liquid moving past the back surface of the statormay be contained or not contained. The back surface of the stator may besealed from the atmosphere or exposed to the atmosphere. The atmospheremay be air or water or other fluid surrounding the actuator. Theenvironment may also be a vacuum, such as is necessary for somemanufacturing processes or the vacuum of space. The back surface of thestator may be configured with cooling fins which increase the surfacearea. These cooling fins may be exposed to a cooling fluid and/or incontact with a heat sink such as the housing or other solid member. Thecooling fins on a stator may have a height greater than 50% of the postwidth in the circumferential direction.

In addition to heat being dissipated from the back surface of thestator, other heat dissipating surfaces may include the surface of apost which may be exposed to a cooling fluid such as air or liquid whichis circulated through a slot such as between a conductor and the post.

Other methods of cooling the stator and/or the conductors may includecooling channels on or below the surface of the stator and/or on orbelow the surface of the conductors. These and other forms of coolingare seen as supplementary to the primary thermally conductive coolingfrom the conductors to the back surface of the stator. In some cases thesupplementary cooling methods may even draw more heat away from thestator than the primary conductive cooling effect, but active coolingmethods require energy and additional cost and complexity, so theconductive cooling path from the conductors to the back surface of thestator is disclosed here as the primary mode of cooling.

For a single actuator producing a fixed torque, the power consumptionrises in the disclosed range, and becomes exponentially larger towardsthe smallest post heights and slot pitches inside the disclosed range.From simulations of the power consumption necessary to produce 100 N mof torque with a single 200 mm average airgap diameter actuator with aradial tooth length of 32 mm and rotor and windings, it can be seen thatthe lowest power consumption occurs outside of the disclosed range, andthat the power consumption increases significantly inside the disclosedrange. In order to minimize power consumption, a designer would be ledtoward larger slot pitch and larger conductor volume devices. Anyactuators using the geometry of the present device will have higherpower consumption than those outside of the disclosed range towardslarger slot pitch and conductor volume values for this type ofapplication.

With the disclosed structure, in which a pole carrier of the electricmachine includes slots and posts, the slots having a slot or pole pitchs and the posts having a height h, in which s is related to h accordingto the disclosed equations, electric excitation may be applied toconductors in the slots with a current density of at least 70 A/mm2.Electric excitations in excess of 70 A/mm² are generally consideredsuitable for the operation of the disclosed device. The cooling effectof having the disclosed slot and conductor structure provides cooling tooffset some or all of the heat generated by the current in theconductors. Any remaining heat generated may be dissipated using one ormore of the disclosed cooling structures or channels. Motors inside thedisclosed range show a reduction of the average flux density in themagnetic flux path for a given electrical input power. This is due, inpart, to the reduced flux path length of the shorter posts and reduceddistance from post to adjacent post through the backiron, as well as thereduced flux leakage between posts. The result is the ability to runhigher current density in motors in the disclosed range without reachingsaturation. The combination of increased cooling capability and lowerflux density at a given current density as compared to motors outside ofthe disclosed range, creates a combination of conditions where highercontinuous torque-to-weight can be achieved for a given temperature at agiven cooling rate, and where the peak momentary torque-to-weight ofmotors in the disclosed range can be significantly higher due tooperating at a lower flux density for a given torque-to-weight in thedisclosed range.

One of the most significant challenges that must be overcome in order toachieve the performance and power consumption benefits of the disclosedgeometry, is to provide a structure that can withstand the immensemagnetic forces that exists between the rotor and stator. Embodiments ofthe disclosed rotor can achieve unusually high flux density in theairgap leading to high attraction forces on the stator posts. At thesame time, achieving the high torque-to-weight of an embodiment of thedisclosed electric machine requires the use of a backiron that has anaxial thickness that, in an embodiment, is less than the circumferentialthickness of the posts (and, in an embodiment, is about half of thethickness of the posts). Furthermore, the axial flux motor configurationdisclosed and the relatively short stator posts of the disclosed rangeresults in an inherently thin stator structure. With a radial fluxmotor, circular laminates with integrated posts can be used. This has aninherent rigidity and naturally provides a desirable flux path along thecircumferential and radial orientation of the laminates. In contrast,the axial flux function of an embodiment of the present device requiresan assembly of individual laminated parts. The result is the need tomanufacture up to hundreds of post components for each actuator, whichincreases manufacturing complexity, time and cost. Furthermore, therelatively thin backiron does not provide an adequate surface area formany potting compounds or adhesives to reliably fix the posts to thebackiron, especially at the high frequency force variation and elevatedtemperatures that are common to electrical machines. As an example, atypical aerospace adhesive that might be used to fix a stator post intoa receiving slot in the stator, might have a heat deflection temperatureof under 80 deg C. for a stress on the epoxy of less than 300 psi.

The back-iron disk of an embodiment can be made of laminates, powderedmetal, or solid metal. The use of laminates has certain advantages,including the possibility of stamped material construction; however; iflaminates are used, they must be attached through means capable ofwithstanding the forces and temperatures of operation of the device.Common methods such as glue may not be sufficient for certain regimes ofoperation where the forces and/or temperatures are high. Nonetheless,laminations may be a good choice for other regimes, and are expected towork well for many high-speed applications.

The use of powdered metal with electrical insulator coating on eachparticle for the back-iron of an embodiment has the advantage ofreducing eddy currents. This coating, however, will typically reduce themagnetic force because it acts like multiple tiny airgaps in the fluxpath. This material is also typically less strong than solid steel oriron with significantly higher creep rate, especially at elevatedtemperatures

A stator manufactured of solid steel typically has high eddy currentlosses. However, geometric features of motors in the disclosed rangehave an eddy current and hysteresis reducing effect that, in someregimes of operation of the an embodiment of the present device, forinstance when operating at speeds which are suitable for robotics, theeddy current losses may be sufficiently low to enable the use of a solidstator. Using solid material is advantageous for strength, rigidity,heat resistance, and fatigue strength. Since embodiments of the presentdevice can often generate sufficient torque to be used without a gearboxin certain applications, the resulting operational speeds may besufficiently low that the eddy current losses be acceptable even with asolid steel stator. Solid cast iron has been found to give sufficientlylow eddy current losses to be practical with some configurations andregimes of operation.

Stators may be constructed of either laminated stacks or a sinteredpowdered metal. An objective of these constructions, as compared to theuse of solid materials, is to reduce the cross sectional area ofelectrically insulated soft magnetic material perpendicular to the fluxpath and thus reduce the generation of eddy currents. Eddy currentsreduce the efficiency by requiring additional input power; they produceextra heat which must be dissipated by the system; and they reduce theoutput torque by creating a damping effect

A single-piece stator fabricated from a solid electrically conductivematerial may be used with embodiments of the disclosed device within thedisclosed ranges of pole density and post height. To avoid eddy currentgeneration, the application should be sufficiently low speed, forexample a duty cycle that consists of 50% (60%, 70%, 80%, 90%) of theoperation at 200 rpm or less for a 175 mm average airgap diameter motorhaving the disclosed range of geometry. By combining this relatively lowspeed range with the relatively small cross sectional geometry of thestator teeth in the disclosed range, the individual stator teeth actsomewhat like laminations and reduce the production of eddy currents.Speeds of less than 200 rpm are generally considered suitable for theoperation of the device. Speeds of less than 100 rpm, less than 50 rpmand less than 25 rpm are also considered suitable for the operation ofthe device.

Additionally, the production of eddy currents is reduced by therelatively short tooth height in the disclosed range. Eddy current andhysteresis losses are volumetric, so the low volume of the presentdevice contributes to the reduction of total iron losses for a givenflux density and switching frequency.

A solid stator, or unitary stator, has a continuous flux path from postto post as shown for example in FIG. 136 and FIG. 137, although,depending on the embodiment, the cooling fins may or may not be present.Each post is thus a portion of the unitary stator. The continuous fluxpath may be provided by a unitary piece of magnetically susceptiblematerial.

The continuous flux path may be provided by a stator made of isotropicmaterials such as ductile iron, steel alloy such as cobalt or siliconsteel, pressed or sintered powdered metal, for example. The metal may beisotropic from post to adjacent post and non-isotropic from a post to abearing race or a post to a member or assembly that connects to abearing, including variable material alloy from backiron to cooling finsand/or to bearings. This can be done by explosion welding or fuseddeposition additive manufacturing, or stir welding or other forms ofcombining dissimilar materials.

The stator may be one piece or unitary from a post to an adjacent postand from a post to a bearing race seat (or bushing seat or contact). Thestator may be unitary from a post to a post and from one of these poststo a member or assembly that is in compression so-as to pre-load abearing or bushing. The stator may be unitary from a post to a post andfrom one of these posts to a member or assembly that is in compressionso-as to pre-load a bearing or bushing and all or part of thecompressive load is a result of magnetic attraction between the statorand a rotor. In cases of pre-loaded bearings, the housing assembly maybe flexible enough to displace the bearing race seat in the direction ofbearing preload past the bearing seat position if the bearing ispresent, by more than 0.002″ if the bearing is not present. In cases ofpre-loaded bearings, the housing assembly may be flexible enough todisplace the bearing race seat in the direction of bearing preload, pastthe bearing seat position if the bearing is present, by more than 0.002″if the bearing is not present and the force exerted on the stator tocause this deformation of the housing is provided at least in part, bythe magnetic attraction of a stator to a rotor.

Performance Benefits of a Solid Stator for Motors in the Disclosed Range

The use of a solid stator in a motor is known to provide the potentialfor cost and manufacturing benefits. Solid stators are not commonlyused, however, because they are known to result in significant eddycurrent losses at typical rotary motor speeds. Eddy currents produceheat, and also have the secondary effect of reducing the torqueperformance of a motor, especially at higher speeds. 50 rpm actuatoroutput is considered high speed for many robotics applications while 200rpm is considered to be very high speed for many robotics applications.Common motors used in robotics are not high enough torque to be used atthe joints as a direct drive actuator, and must be used without atorque-increasing gearbox. The result of using a torque increasinggearbox is the need to operate the motor at much higher speeds than theactuator output. Eddy current losses increase exponentially with speed,so the use of a solid stator for a robotic actuator would be expected toresult in very poor performance.

Laminates or electrically insulated powdered material are commonly usedin motors to provide low eddy current characteristics at the speedsnecessary to drive a torque increasing gearbox at output speeds suitablefor robotics. But while the need to use laminates or electricallyinsulated powdered material has been shown to be beneficial forexemplary motors outside the claimed range, motors inside the claimedrange exhibit an unexpected benefit in terms of eddy current andhysteresis reduction to the point where the use of a laminate materialwould actually be detrimental to performance in motion controlapplications such as robotics.

Analysis Set-Up

To demonstrate this unexpected benefit, a series of motors was simulatedto show eddy current and hysteresis losses at 200 rpm and for a range ofmotors starting at low pole density and increasing pole density into thedisclosed range. Simulations have shown that for an exemplary motorseries with a concentrated flux rotor embodiment of the present device,the PM flux from the rotor is responsible for approximately 80% or moreof the total eddy current and hysteresis loss in the stator at currentlevels up to 19.7 Arms/mm². The non-powered eddy current losses with therotor spinning at 200 rpm are, therefore, used as a reliable indicatorof overall loss over a reasonable range of applied current densities.

Reversing Stator Loss Trend

FIG. 183 shows the eddy current and hysteresis losses of a two solidstator materials compared to the eddy current and hysteresis losses of alaminated stator for a series of exemplary motors having the same aspectratio of post height to slot pitch, and the same radial post length. Thelosses are simulated or calculated as described above, at a rotor speedof 200 rpm with no current applied. Note that M19 electrical steel wasused in the simulation for one of the solid stator materials for thesake of direct comparison with the M19 laminated stator even though itis not commonly available in plate or block form. Other materials whichare available in plate or block form, or which can be cast to near netshape parts are available in industry with similar magnetic performancecharacteristics to M19.

Referring now to FIG. 183, it can be seen that the higher frequencyrequired for higher pole numbers at a given speed result in the expectedexponential increase of losses in the laminated stator series toward andinside of the disclosed range. As would also be expected, much higherlosses are shown in a solid stator as compared to a laminated stator formotors with large pole pitch as shown at the far right of the graph.These losses then increase at a much greater rate than the laminatedstator, as pole pitch is decreased from the right side toward the middleof the graph as drive frequencies must increase. As the pole pitchapproaches the claimed range, however, the eddy current magnitude doesnot continue to increase like it does in the laminated stator series.This is because the thinner flux path cross section of motors toward thedisclosed range, along with the reduced eddy currents and hysteresislosses that result from the reduced stator volume toward the claimedrange, become dominant in the overall effect, and the trend towardincreasing losses is reversed. This reversal of the expected trendresults in a total eddy current and hysteresis loss with a solid statorin the disclosed range that drops below anywhere else in the exampleseries.

Increased Torque-to-Weight

Although the losses shown in this analysis in FIG. 183 are always higherwith a solid stator as compared to a laminated stator, for the motors inthe disclosed range, the reversing of this trend is significant enoughto result in improved torque-to-weight performance up to approximately200 rpm with a solid stator than with a laminated stator as shown inFIG. 188. This very higher torque-to-weight of motors in the disclosedrange is shown to be high enough that they can be used as direct-driveactuators at the robot joints without the need for a torque-increasinggearbox. This creates a situation where the very high torque-to-weightof the present device enables, and at the same time benefits from, theuse of a solid stator. It enables the use of a solid stator by allowingit to operate as a direct drive actuator at the robot joints and atoperating speeds that are considered high speed for a direct driveactuator but low enough to take advantage of the present device lossreducing geometry. At the same time, motors in the claimed range benefitfrom the use of a solid stator by increasing the torque-to-weight beyondwhat is possible with a laminated stator of the same material.

Torque-to-Weight Analysis Set-Up

The reduction in torque-to-weight due to eddy current losses wascalculated by simulation at speeds up to 200 rpm. The torque-to-weightof a 24 slot approximation of a device outside the claimed range withapplied current densities of and 6 A/mm² is shown to be below thelaminated stator at very low speeds and to continue dropping evenfurther below the laminated stator up to 200 rpm

The torque-to-weight for a 108-slot approximation of the present deviceis shown to start significantly higher than the laminated stator due torigidity requirements necessitating a thicker backiron to maintain theairgap in the laminated case. The solid stator however is sufficientlyrigid at the minimum backiron thickness and needs no extra materialadded. Additionally, the stall torque of the solid stator is slightlyhigher due to having increased magnetic material in the samecross-sectional area of the magnetic flux path.

Note that an applied current density of 19.7 A/mm². was chosen for the108 slot motor of the present device because it yields a similar powerconsumption to the 24 slot motor at 6 A/mm² at stall torque conditions.

It is not surprising that the torque to weight is almost immediatelydrops below the zero speed torque-to-weight for the exemplary motor withlow slot density. For the exemplary motor inside the disclosed range,however, the torque-to-weight is significantly higher at zero speed dueto the ability to maintain rigidity with a minimum backiron thickness,combined with the higher material density that results from the 100%magnetic material density compared to the laminations which have apercentage of the flux path occupied by non-magnetic insulation layersand adhesives. As the speed increases, the torque-to-weight still dropsoff with the present device as it does with the low slot density motor,but it stays above the laminated motor torque-to-weight all the way upto 200 rpm. Considering that 200 rpm is extremely high speed forrobotics applications, and considering the other potential benefits of asolid stator in terms of the reduced cost and increased stator strengthand rigidity, the present device is able to provide the known benefitsof a solid stator without a reduction to torque-to-weight when used inrobotics or other applications with similar speed and torque-to-weightrequirements.

In Depth Description

An in-depth description of how the above analysis was carried out is asfollows. A 3-D simulation was conducted using MagNet™ software byInfolytica™. A linear approximation of an axial flux machine havinggeometry within the claimed ranges having 108 slots and 110 poles wasconstructed and simulated using the Transient with Motion™ solver topredict the losses in solid and laminated stators. A similar simulationwas done using a geometry outside of the claimed range with anequivalent of 24 slots and 26 poles in the same diameter. The simulationpredicts the eddy current and hysteresis loss in laminated structuresusing an analytical application of the Steinmetz equation. In solidstructures the eddy current loss is predicted by the simulation usingthe average of the ohmic loss in the structure based on the resistivityof the material. One series, namely Durabar 65-45-12, used the softwareto generate the eddy current magnitude, and the other solid eddy currentmagnitude was estimated based on a multiplication by the ratio of theirrespective resistivities. For 24 gauge M-19 electrical steel, thehysteresis loss of the solid was assumed to be equal to that of thelaminated equivalent, however the author acknowledges that in realitythe hysteresis loss in a solid block of a material will be greater thanin a laminated stack. Still, the majority of the losses at speed are dueto eddy currents which are the focus of this study therefore thisassumption is believed to be adequate for the purposes of this study.For the solid Durabar 65-45-12 the hysteresis loss was analyticallycalculated using an estimate based on experimental measurements whichfound the loss to be approximately 5062 J/m³ and the frequency exponentwas assumed to be 1.1. The volume of magnetically active material in thestator was estimated to be the volume of the teeth plus a portion of thebackiron equal in depth to the width of an individual tooth, based onsimulation results. Therefore, for Durabar the hysteresis loss wascalculated as follows:

P _(hyst-Dura)=5062·V _(active) ·f ^(1.1)

Where P_(hyst-Dura) is the power loss due to hysteresis in Durabar65-45-12, V_(active) is the magnetically active volume of the stator,and f is the primary magnetic switching frequency. For any device, theprimary magnetic switching frequency is related to the output speed andthe number of poles according to the following relationship:

$f = {\frac{RPM}{60} \cdot \frac{N_{p}}{2}}$

Where RPM is the output speed of the device in revolutions per minute,and N_(p) is the number of poles.

The reduction in torque due to hysteresis losses was calculated based onthe reduction in torque due to eddy current losses as calculated by thesimulation. The resultant torque for a 108-slot approximation of thepresent device and a 24 slot approximation of a device outside theclaimed range with applied current densities of 19.7 Arms/mm² and 6A/mm² are shown in FIG. 187 and FIG. 184 respectively.

FIG. 183 shows eddy current and hysteresis losses of a solid statorcompared to the eddy current and hysteresis losses of a laminated statorfor a series of exemplary motors having the same aspect ratio of postheight to slot pitch, and the same radial post length. The losses aresimulated or calculated as described above, at a rotor speed of 200 rpmwith no current applied. It can be seen that while the losses of alaminated stator increase exponentially toward and inside of the claimedrange, motors with solid stators initially show increased losses whenmoving from large slot pitches towards the left to smaller slot pitchesas the driving frequency increases. However the combined effect ofrestricting eddy current flow in narrower teeth and reducing toothvolume offsets the effects of increased frequency and begins to reducethe overall losses as the slot pitch continues to decrease. Thisreversing trend shows the non-obvious benefit of combining a solidstator with the claimed geometry range for acceptable losses in roboticsapplications where speeds are relatively low.

Simulations have shown that for an exemplary motor series with a rotorembodiment of the present device, the PM flux from the rotor isresponsible for approximately 80% or more of the total eddy current andhysteresis loss in the stator at current levels up to 19.7 Arms/mm². Thenon-powered eddy current losses with the rotor spinning at 200 rpm can,therefore, be used as an adequate indicator of overall loss over areasonable range of applied current densities. The data in FIG. 183shows the sum of the eddy current and hysteresis losses for three motorseries across a range of slot pitches at a rotor speed of 200 rpm withno current applied.

Much higher losses are shown in a solid stator as compared to alaminated stator at 200 rpm in FIG. 183 for motors with large slotpitch, with these losses increasing dramatically as slot pitch isdecreased. At a certain point, however, the eddy current reducingbenefits of thinner cross sections becomes dominant in the overalleffect, and the trend toward increasing losses is reversed. This trendreversal shows a total eddy current/hysteresis loss with a solid statorin the claimed range that drops significantly below anywhere else in theexample series. The losses are always much higher than a laminatedstator, but other factors are also in effect that make these lossesacceptable.

As a baseline comparison, a simulation was performed for an exemplarygeometry outside of the present device range with much larger widerposts, having 24 slots and 26 poles for the same average airgapdiameter, and possessing the same aspect ratio of tooth width to heightas the present device example. The radial length of the teeth was keptconstant compared to the present device example so that both motorsrepresent the same outer and inner diameters. The results shown in FIG.184 for a typical applied current density of 6 A/mm², show that even atthese relatively low speeds, the torque in the solid stator dropssignificantly, by a factor of 31%, while the torque in the laminatedstator only drops marginally. Similarly, the losses due to eddy currentsin the example geometry outside of the claimed range are larger than anyof the other system losses as shown in FIG. 185.

To demonstrate the practical use of the present device with a solidstator, an analysis was created and recorded in FIG. 186 and FIG. 187 tosimulate a motor with the same OD as in FIG. 184 and FIG. 185 but withgeometry in the claimed range as described above. The applied currentdensity was 19.7 A/mm² which yields a similar power consumption to thedevice in FIG. 185 for stall torque conditions (speed of 0 rpm).

The individual and total stator losses in the solid M-19 stator areshown in FIG. 186. Although the eddy current losses increasedramatically with speed, the resistive losses in the conductorsrepresent the majority of the loss, all the way up to 200 rpm in thisexample. The geometry of the present device results in eddy currentlosses that remain below what is considered, by the inventor, to beacceptable for up to what would be considered high speed for an actuatorin a robotic application, especially in view of the many other potentialbenefits of using a solid stator.

At speeds above 200 rpm the eddy current losses continue to increaseexponentially and become unacceptably large for many applications evenfor geometries within the benefit range. Therefore, a solid stator usingthe present geometry would be impractical for many typical direct-drivemotor applications which include operating speeds of greater than 200rpm for this size of motor. It is the combination of the relatively lowspeed range (as compared to typical direct drive motor applications) oftypical of robotics applications with the present device geometry thatallows a solid stator to be usefully implemented.

One of the benefits of a solid stator is the ability to increase thetorque-to-weight of the present device as a result of the much highermechanical strength of a solid material as compared to a laminated orinsulated powdered material. Outside of the claimed range, as in theexample geometry of FIG. 185, the thickness of the stator backironnecessary for optimum magnetic properties also provides sufficientstiffness such that laminated and solid stators will have the samevolume. However in the claimed range, the minimum backiron thickness mayneed to be increased in the case of a laminated or powdered sinteredstator to prevent the attraction of the rotor magnets from deforming thestator and closing the airgap in certain cases when small airgaps and/orstrong rotor magnets are used. In the comparison in FIG. 188, verystrong NdFeB N52 permanent magnets were used in the rotor, therefore thelaminated stator in the present device range was given twice thethickness of that of the solid stator as an estimate, however dependingon the method of bonding the laminations this thickness may need to beincreased even more. Therefore, a solid stator will typically yield thehighest torque-to-weight in the present device range for speeds up to,for example, 200 rpm by either allowing stronger rotor magnets to beused for the same backiron thickness thereby increasing the torque, orby allowing thinner backiron to be used for the same rotor magnetsthereby decreasing the weight. Increasing torque-to-weight has powerconsumption benefits that are described elsewhere in this disclosurewhich can partially or completely offset the additional eddy currentlosses up to reasonably high speed for many robotic applications. Asolid stator also reduces the cost by reducing processing time and insome cases even allowing lower cost materials and processes such as caststeel parts.

In addition to the structural and manufacturing cost benefits, a solidstator can also provide higher static torque than a laminated stator ofthe same material. As shown in FIG. 187, the solid M-19 stator provideshigher static torque than the laminated M-19 stator due to the absenceof insulation between the laminations which comprises approximately 5%of the volume of the laminated stator. As a result of the initiallyhigher static torque, combined with the low cross sectional area of thepresent device, the solid M-19 stator may provide higher torque than alaminated equivalent potentially up to 50 rpm or more. 50 rpm is lowspeed for a common electric motor, but it is considered to be reasonablyhigh speed for many robotic applications. If the duty cycle of a robotis an average of 50 rpm with a maximum speed of 100 rpm, for example,the average efficiency and torque of the solid M-19 stator may besimilar to that of the laminated M-19 stator in this example. At 200rpm, which is considered to be very high speed for many roboticsapplications, the torque of the exemplary embodiment with a solid statoris lower than that using the laminated stator by approximately 9%. Thisis only ⅓ of the loss of torque at this speed found in the exemplaryembodiment in FIG. 184 using the same comparison of a solid vs laminatedstator and is considered to be acceptable loss in view of the otherbenefits of a solid stator, such as lower cost and increased structuralintegrity which allows for lower weight. A direct comparison of thetorque of the two embodiments is shown in FIG. 189 and a directcomparison of the total losses in both embodiments is shown in FIG. 190.It should be noted that M-19 electrical steel is not typically availablein solid form, but is used here as a direct comparison for illustrativepurposes. Many different alloys can be formulated and used as a solidmaterial with the present device. The addition of increased amounts ofsilicon can, for example, can be used to further reduce eddy currents ina solid stator material. The addition of extra silicon may reduce thestatic torque but may reduce the losses at higher speeds as anacceptable compromise. The ideal performance characteristics of a solidstator material will depend on the specific application but can bedetermined by someone skilled in the art by applying the principlesdisclosed here.

Durabar 65-45-18 ductile iron is shown as another non-limiting exampleof a solid material that can be used for the stator. This material ishighly machinable and has been used in various prototypes. It has alower static torque than the same stator made from M-19 but similarlosses as speeds increase. At 200 rpm, the torque and efficiency arestill considered to be adequate to provide very high torque-to-weightand acceptable power consumption.

The solid stator may be used with machines having sizes within thebenefit space, and with airgaps of different sizes but within practicallimitations such as having for example a thickness with the range 0.005″to 0.010″, depending on the magnetic forces across the airgap andstrength of the materials used. Simulations at 0.010″ gap showed thatfor most of the disclosed ranges, greater than 75% of the area of thatrange shows a KR benefit at 0.01″ gap. The only ones which show lessbenefit are the smallest sizes as the highest KR, namely at or betweensets of inequalities A2 and A3. Therefore, a benefit is found for gapsfrom 0.001″ up to 0.01″ for all motors. Back iron thickness may be 50%or less of the axial thickness of the circumferential thickness of theposts, for an axial flux machine, but this value is variable. Thickerback iron results in loss of KR, while thinner back iron results in lossof strength

The stator may be made from any metal or metal alloy that is heat formedand has a yield strength above 30,000 or 40,000 psi, for example siliconsteel, cobalt alloys, ductile iron or other soft magnetic alloy, and nomeasurable creep below 20,000 psi stress. For a 200 mm Average airgapdevice rotation speeds should not exceed 100 rpm for the majority of thetime or exceed 200 rpm for more than 25% of the time, or be above 50 rpmaverage speed for best results of using a solid stator. Embodiments withunitary stator benefit from being run at speeds of less than 200 rpm,100 rpm, 50 rpm or 25 rpm.

Electric machines within the benefit space also provide very high peaktorque and very high safety stop capability. Such electric machines showa reduction of the flux density for a given electrical input power. Thisis due, in part, to the reduced flux path length of the shorter postsand reduced distance from post to post through the backiron, as well asthe reduced flux leakage between posts. The result is the ability to runhigher current density in motors in the disclosed range without reachingsaturation. The combination of increased cooling capability and lowerflux density at a given current density as compared to motors outside ofthe disclosed range, creates a combination of conditions where highercontinuous torque can be achieved for a given temperature at a givencooling rate, and where the peak momentary torque-to-weight of motors inthe disclosed range can be significantly higher due to operating at alower flux density for a given torque-to-weight in the benefit space.

Electric machines in the benefit spaced have reduced material volumeresulting in reduced manufacturing cost and reduced manufacturingimpact. The magnets may be magnetically retained (even though theirnatural state is to be repelled or partially repelled from slots) by thefollowing, extra deep magnets and cut-outs in opposite end of postscreates inward bias despite majority of flux linking through airgap.

For application of the disclosed geometry to motor types such astransverse flux motors, there may be other design considerations thatwill affect the extent to which the heat dissipation and otheradvantages in the disclosed range are realized. For a transverse fluxmotor, for example, the width of the posts (in a direction parallel tothe axis of the coil) is independent of the pole pitch. This width,however, is very important to determine the weight of the system becauseit is directly related to the necessary thickness of stator backiron.One must also consider the ratio of the axial width of the post to theaxial width of the coil. If these quantities are decreased, the totalairgap surface area and conductor cross-sectional area can be heldconstant by arraying the entire assembly axially. Therefore, the optimumtorque-to-weight and heat dissipation will also depend on the arraypitch and post axial width.

Power and Cooling Figure

As shown in FIG. 191, an actuator 3400 may be cooled using coolingsupply 3402. Cooling supply 3402 may provide a fluid flow for coolingactuator 3400 via flow channel 3404. The cooling supply may be connectedto any of the flow channels disclosed, including interior of any housingor openings, or on the stator or rotor or any disclosed carrier.Actuator 3400 may also be supplied with power (electrical excitation) bypower supply 3406. Power supply 3406 may supply power to actuator 3400using power connector 3408.

Ultralight Embodiment

The views shown in FIG. 182 to FIG. 199B are of a simplified drawing ofself-contained actuator assembly according to the principles disclosed.It uses bushings instead of bearings which has cost and weight benefitsand is suitable for many applications where lower speeds and or shortservice life are typical. Note that conductors are not shown in any ofthe images and can be of any type including those disclosed here forother embodiments.

Referring to FIG. 192, the embodiment of an actuator 3500 shown here hasexternal stators 3502 on either side of an internal rotor 3504. Inanother embodiment, there can be an internal stator with external rotorson either side, but this is not considered desired for cooling. Theactuator shown moves an output ring 3506 relative to a fixed ring 3508.In the embodiment shown, the output ring 3506 is at the inner diameter(ID) of the actuator and the fixed ring 3508 is at the outer diameter(OD), but in another embodiment, the output ring could be at the outerdiameter and the fixed ring at the inner diameter.

Bushings or low friction coatings may be used to minimize frictionbetween the rotor 3504 and stators 3502, as shown in FIG. 193A. As seenmore clearly in the closeup of FIG. 193B, the embodiment shown has axiallocation bushings or low friction coating 3510 in the airgap betweeneach stator 3502 and the rotor 3504, and radial location bushings or lowfriction coating 3512 between the rotor 3504 and fixed ring 3508.

As shown in FIG. 194, the stators 3502 have posts 3514. The posts 3514may be oriented radially and may have axial extensions/spacers 3516 fromthe outer diameter ends of the posts. These extensions 3516 arepreferably made of one piece with the stator posts 3514 and back iron3518. This provides high rigidity in the axial direction as well as totransfer torque to the fixed ring 3508. By using the post tips as axialspacers it allows the insertion of conductor coils onto the postswithout interference. As indicated by the arrows labeled with referencenumeral 3520, the stators will flex inwards as a result of magneticattraction between the stators and rotor, particular towards the innerdiameter of the stator in the embodiment shown. The shape of the statorand/or rotor can be preformed so as to, when taking into account themagnetic attraction, achieve any desired airgap such as a reasonablyconsistent airgap from ID to OD of airgap space between stator androtor. FIG. 195 shows a closeup of stator posts 3514 with more arrows3520 showing a direction of flexing.

As shown in FIG. 196, rotor 3504 in the embodiment shown comprises apermanent magnet (PM) carrier 3522 holding an array of permanent magnets(PMs) 3524. In the embodiment shown, the PM carrier is a concentratedflux PM rotor carrier with a rotor backiron 3526. Output ring 3506 Rotoroutput ring is fastened to ID of PM carrier 3522 (or OD in OD outputconfiguration) with for example a press fit, adhesive, or fasteners etc.As can also be seen in this figure, the fixed ring 3508 in thisembodiment has slots 3532 for receiving the axial extensions 3516 of thestator posts.

FIG. 197 shows the PM magnet carrier 3522 of this embodiment without PMmagnets. The PM carrier has posts 3528 and backiron 3526, all preferablymade of a one piece isotropic material such as a steel alloy or ironalloy. Flux restriction bores 3530 are placed in the backiron betweenposts.

FIG. 198 shows the shape of the OD ends of stator posts 3514 moreclearly including the extensions 3516. In an alternative OD outputembodiment (not shown), the extensions may be at the ID ends of theposts.

FIG. 199A and FIG. 199B show for illustrative purposes an overlappingpattern of rotor posts 3528 and stator posts 3514. By implementing arotor post-to-stator post difference of 4, or more, and by ensuring thatat least part of the circumferential width of the stator or rotor postsis wider than the gap in the other member, a continuous or nearlycontinuous overlap of the posts can be achieved. A 4 post difference isshown here, a higher or lower difference such as 2 or 6 or more can beused with various effects.

The active magnetic components of an electric machine in the disclosedrange can be inserted into a system as a frameless motor or supported bybearings and other structure in a framed motor or actuator. An unusuallythin flux path cross section from post to post is inherent in thedisclosed range geometry. This thin section geometry provides for thepotential to construct the stator out of an isotropic soft magneticmaterial such as an iron alloy or steel alloy with the surprising resultof increased performance and/or efficiency at speeds which are suitablefor many robotic applications. An isotropic soft magnetic material alsoprovides the structural strength, stiffness, and creep resistance toachieve and maintain the unusually small airgap required to achieve ahigh percentage of the potential torque.

There are many ways to configure the support structure and bearingsbetween the stator and rotor of embodiments of an electric machinedisclosed here. Some of these will be known to someone skilled in theart. Spacer extensions are preferably fixed in the spacer ring with apress fit or engagement feature (not shown in figures) to add rigidityto the stators. Others are shown here which take advantage of theunusually rigid structure provided by an isotropic rotor and statorassembly. The embodiment shown here provides a self-contained actuatorhousing and bearing structure with minimal weight cost and complexity.

By using the inherent rigidity of the isotropic stators, it is possibleto support the stators with an axial spacer such that they are preventedfrom pulling together on the ID or the OD of the stators. In anembodiment the spacer is formed or machined as one piece with the statorin the form of extended sections on the OD or ID of the stator posts.These spacer extensions can contact each other or an intermediate spacerring as shown here. In certain applications the magnetic attractionforce between the stators and the rotor may be enough to hold theassembly together without the need for additional fasteners oradhesives. In an exemplary embodiment with a 200 mm outside diameter,the magnetic attraction between the stator and rotor can be up to orgreater than 400 kg per stator/rotor airgap. The construction shown hereprovides enough rigidity to result in an average stator ID displacementtowards the rotor of 0.001″ to 0.003″. The stators and rotor may bepreformed such that this displacement will not cause pressure on thebushings or non-slip coating shown. With a four post difference betweenthe stator and rotor, four equally spaced magnetic attraction zones canbe realized for a reasonably consistent force on a stator. A low costand light weight bearing configuration is shown here with low frictionbushing material such as Teflon in the air gap between the stator androtor, and around the OD of the rotor. A low friction coating on thestator and or rotor can be used as well. FIG. 199A and FIG. 199B show anon-limiting example of a stator and rotor post geometry which providesthat preferably all or a high percentage (such as 50% or higher althougha lower percentage may also provide enough overlap) of the stator postsoverlap with a rotor post at all times. This high percentage ofoverlapping posts provides a consistent support between the stator androtor allowing a low friction coating or intermediate bushing materialto keep the rotor centred between the stators.

A small amount of flexibility in the stator can be useful to minimize oreliminate play between the stator and rotor while still allowing forheat expansion and variations in manufacturing tolerance.

A diamond like coating (DLC) or other low friction, low wear ratecoating can be applied to the stator and rotor post tips.

There are many materials that can be used for the stator and rotor. Anexemplary material in terms of cost and performance is ductilecast-iron. The small amount of flexibility in the stator that isproduced by the magnetic attraction can be used to preload the statorand rotor post faces together. The stator and/or rotor can be pre-formedwith a slightly conical shape to achieve a parallel or other air gapgeometry.

What is claimed is:
 1. An electric motor comprising a stator comprisingelectromagnetic elements, the stator having posts on one side and abackiron having cooling fins on an opposite side, the stator comprisinga unitary piece of material including at least portions of the posts andat least portions of the cooling fins.
 2. An electric motor comprising arotor arranged for rotation relative to one or more stators comprisingelectromagnetic elements, the rotor comprising a permanent magnetcarrier loaded with permanent magnets, an output ring, and bearings forsupporting the rotor for rotation, the bearings located intermediatebetween the permanent magnet carrier and the output ring.
 3. Theelectric motor of claim 2 in which the motor is an axial flux motor, andthe one or more stators are two stators and the rotor is arrangedbetween the two stators.
 4. The electric motor of 3 in which thebearings are preloaded by magnetic forces between the rotor and stators.5. The electric motor of claim 3 in which the rotor has two axial sides,and comprises magnets on each axial side of the rotor, the magnets oneach axial side oriented tangentially, and each magnet aligned axiallywith a respective magnet on the other axial side, the tangentialorientation of each magnet being opposite to the tangential orientationof the respective magnet on the other side.
 6. The electric motor ofclaim 2 in which the one or more stators comprise spiral cooling fins.7. An electric motor comprising a rotor arranged on bearings forrotation between two stators from which the rotor is separated byairgaps, a magnetic force between the rotor and stators attracting thestators to the rotor and applying a preloading force on the bearings. 8.The electric motor of claim 7 in which the rotor has an output ringlocated radially inward from the magnets.
 9. The electric motor of claim8 in which the bearings have outer diameter (OD) races attached to therotor.
 10. The electric motor of claim 7 in which the rotor has anoutput ring located radially outward from the magnets.
 11. The electricmotor of claim 10 in which the bearings have inner diameter (ID) racesattached to the rotor.
 12. The electric motor of claim 7 in which theairgaps will close by more than 50% as a result of magnetic force if thebearings are not present in the assembly.
 13. The electric motor ofclaim 7 in which the stators and rotor will come into contact if thebearings are not present in the assembly.
 14. The electric motor ofclaim 7 in which there are axial inward facing surfaces of a housing andthe bearings have axial outward facing bearing races contacting theaxial inward facing surfaces of the housing, and the axial inward facingsurfaces of the housing deform under magnetic load such that thedifference in position between the position of the axial inward facingsurfaces and a hypothetical position of the inward facing surface if nobearings are present is greater than 0.002″.
 15. The electric motor ofclaim 7 in which there are axial inward facing surfaces of a housing andthe bearings have axial outward facing bearing races contacting theaxial inward facing surfaces of the housing, and the axial inward facingsurfaces of the housing deform under magnetic load such that thedifference in position between the position of the axial inward facingsurfaces and a hypothetical position of the inward facing surface if nomagnets are present in the rotor is greater than 0.002″.
 16. Theelectric motor of claim 1 in which the posts have a post width in thecircumferential direction, and the backiron including the fins have aheight greater than 50% of the post width.
 17. The electric motor ofclaim 1 in which the fins have tips comprising a different material thanthe unitary piece of material.
 18. The electric motor of claim 1 inwhich the electric motor is an axial flux motor.
 19. The electric motorof claim 18 in which the cooling fins are spiral shaped.
 20. Theelectric motor of claim 1 further comprising: a rotor havingelectromagnetic elements defining magnetic poles, the rotor beingarranged to rotate relative to the stator, the magnetic poles having apole pitch S in mm; an airgap between the stator and the rotor; posts ofthe stator having a post height in mm; the stator and the rotor togetherdefining a size of the electric machine; the size of the motor, polepitch and post height being selected to fall within a region in a spacedefined by size, pole pitch and post height, the region being defined byeither 1) a first union of: a) a first surface defined by a first set ofinequalities for a first size of electric machine; b) a second surfacedefined by a second set of inequalities for a second size of electricmachine; and c) a set defined as containing all points lying on linesegments having a first end point on the first surface and a second endpoint on the second surface; the first set of inequalities and thesecond set of inequalities being respectively sets of inequalities A andB, or B and C, or C and D, in which the group of inequalities A is for asize of 25 mm, the group of inequalities B is for a size of 50 mm, thegroup of inequalities C is for a size of 100 mm, the group ofinequalities D is for a size of 200 mm; or 2) a second union of asurface as defined by set of inequalities D and a corresponding set ofall points with size greater than the surface but with pole pitch andpost height corresponding to points within the surface; where A isselected from the group of sets of inequalities consisting of: Set A1:Post Height> −1.070*S + 2.002  for 0.572 < S < 1.189  1.175*S + −0.667for 1.189 < S < 2.269 13.502*S − 28.637 for 2.269 < S < 2.500 PostHeight< −5.898* S + 19.863  for 1.970 < S < 2.500 0.229*S + 7.794 for1.349 < S < 1.970 7.607*S − 2.160 for 0.723 < S < 1.349 11.430* S −4.924  for 0.572 < S < 0.723

Set A2: Post Height> −1.340*S + 2.305  for 0.619 < S < 1.120 1.100*S −0.429 for 1.120 < S < 2.074 3.830*S − 6.082 for 2.074 < S < 2.269 PostHeight< −69.510*S + 160.318 for 2.222 < S < 2.269 −3.430*S + 13.492 for1.667 < S < 2.222 2.830*S + 3.056 for 1.133 < S < 1.667 8.650*S − 3.545for 0.619 < S < 1.133

Set A3: Post Height> −4.160*S + 5.032  for 0.723 < S < 0.967 0.839*S +0.198 for 0.967 < S < 1.692 2.713*S − 2.973 for 1.692 < S < 1.939 PostHeight< −53.233*S + 105.506 for 1.879 < S < 1.939 −1.406*S + 8.122  for1.465 < S < 1.879 3.898*S + 0.353 for 1.035 < S < 1.465 7.535*S − 3.412for 0.723 < S < 1.035

B is selected from the group of sets of inequalities consisting of: SetB1: Post Height> 0.254*S + 0.462  for 0.319 < S < 3.667 2.665*S + −8.380for 3.667 < S < 5.000 Post Height< −18.282*S + 96.357  for 4.500 < S <5.000 −4.663*S + 35.071  for 2.738 < S < 4.500 2.585*S + 15.227 for1.447 < S < 2.738 16.013*S − 4.204  for 0.319 < S < 1.447

Set B2: Post Height> 0.269*S + 0.456 for 0.380 < S < 3.016 3.051*S −7.936 for 3.016 < S < 4.167 Post Height< −14.766*S + 66.309  for 3.667 <S < 4.167 −3.952*S + 26.654 for 2.315 < S < 3.667  3.108*S + 10.310 for1.278 < S < 2.315 14.542*S − 4.303  for 0.389 < S < 1.278 88.444*S −33.051 for 0.380 < S < 0.389

Set B3: Post Height> 0.191*S + 0.626 for 0.472 < S < 2.181 2.135*S −3.613 for 2.181 < S < 3.095  53.475*S − 162.511 for 3.095 < S < 3.175Post Height< −5.095*S + 23.450 for 2.222 < S < 3.175  0.805*S + 10.339for 1.381 < S < 2.222 10.251*S − 2.706  for 0.572 < S < 1.381 24.420*S −10.810 for 0.472 < S < 0.572

C is selected from the group of sets of inequalities consisting of: SetC1: Post Height> 0.322*S + 0.359 for 0.233 < S < 6.667  2.202*S − 12.179for 6.667 < S < 8.333 Post Height< −25.555*S + 219.122 for 7.778 < S <8.333 −5.585*S + 63.794 for 4.000 < S < 7.778  3.214*S + 28.600 for1.793 < S < 4.000 21.749*S − 4.633  for 0.233 < S < 1.793

Set C2: Post Height> 0.277*S + 0.593 for 0.250 < S < 5.182  2.342*S −10.111 for 5.182 < S < 7.222 Post Height< −13.149*S + 101.763 for 6.111< S < 7.222 −4.885*S + 51.265 for 3.333 < S < 6.111  4.291*S + 20.680for 1.520 < S < 3.333 20.788*S − 4.395  for 0.251 < S < 1.520 161.000*S− 39.588  for 0.250 < S < 0.251

Set C3: Post Height> 0.277*S + 0.591 for 0.278 < S < 4.425 1.916*S −6.663 for 4.425 < S < 6.111 Post Height< −21.337*S + 135.438 for 5.556 <S < 6.111 −4.985*S + 44.588 for 3.175 < S < 5.556  2.749*S + 20.031 for1.560 < S < 3.175 18.321*S − 4.260  for 0.278 < S < 1.560

and D is selected from the group of sets of inequalities consisting of:Set D1: Post Height> 0.257*S + 0.327 for 0.208 < S < 7.778   1.977*S −13.044 for 7.778 < S < 9.444 Post Height< −36.195 *S + 347.445  for8.889 < S < 9.444 −5.777 *S + 77.062  for 4.833 < S < 8.889  1.950 *S +39.718 for 2.222 < S < 4.833 20.301 *S + −1.058 for 0.389 < S < 2.22234.481 *S + −6.574 for 0.208 < S < 0.389

Set D2: Post Height >  0.322 * S + 0.359 for 0.233 < S < 6.667  2.202 *S + −12.179 for 6.667 < S < 8.333 Post Height < −25.555 * S + 219.122for 7.778 < S < 8.333  −5.585 * S + 63.794 for 4.000 < S < 7.778 3.214 * S + 28.600 for 1.793 < S < 4.000   21.749 * S + −4.633 for0.233 < S < 1.793

Set D3: Post Height >  0.212 * S + 0.600 for 0.264 < S < 4.833  3.017 *S + −12.960 for 4.833 < S < 6.667 Post Height < −12.356 * S + 89.531 for5.556 < S < 6.667  −4.551 * S + 46.170 for 3.175 < S < 5.556  3.850 *S + 19.496 for 1.502 < S < 3.175   19.751 * S + −4.387 for 0.264 < S <1.502


21. The electric motor of claim 2 in which: the electromagnetic elementsof the stator include posts, with slots between the posts, one or moreelectric conductors in each slot, the posts of the stator having a postheight in mm; the permanent magnets of the rotor define magnetic poles,the magnetic poles having a pole pitch S in mm; the stator and the rotortogether defining a size of the electric machine; there is an airgapbetween the first carrier and the second carrier; and the size of themotor, pole pitch and post height is selected to fall within a region ina space defined by size, pole pitch and post height, the region beingdefined by either 1) a first union of: a) a first surface defined by afirst set of inequalities for a first size of electric machine; b) asecond surface defined by a second set of inequalities for a second sizeof electric machine; and c) a set defined as containing all points lyingon line segments having a first end point on the first surface and asecond end point on the second surface; the first set of inequalitiesand the second set of inequalities being respectively sets ofinequalities A and B, or B and C, or C and D, in which the group ofinequalities A is for a size of 25 mm, the group of inequalities B isfor a size of 50 mm, the group of inequalities C is for a size of 100mm, the group of inequalities D is for a size of 200 mm; or 2) a secondunion of a surface as defined by set of inequalities D and acorresponding set of all points with size greater than the surface butwith pole pitch and post height corresponding to points within thesurface; where A is selected from the group of sets of inequalitiesconsisting of: Set A1: Post Height > −1.070 * S + 2.002 for 0.572 < S <1.189  1.175 * S + −0.667 for 1.189 < S < 2.269 13.502 * S − 28.637 for2.269 < S < 2.500 Post Height < −5.898 * S + 19.863 for 1.970 < S <2.500  0.229 * S + 7.794 for 1.349 < S < 1.970  7.607 * S − 2.160 for0.723 < S < 1.349 11.430 * S − 4.924 for 0.572 < S < 0.723

Set A2: Post Height >  −1.340 * S + 2.305 for 0.619 < S < 1.120  1.100 *S − 0.429 for 1.120 < S < 2.074  3.830 * S − 6.082 for 2.074 < S < 2.269Post Height < −69.510 * S + 160.318 for 2.222 < S < 2.269  −3.430 * S +13.492 for 1.667 < S < 2.222  2.830 * S + 3.056 for 1.133 < S < 1.667 8.650 * S − 3.545 for 0.619 < S < 1.133

Set A3: Post Height >  −4.160 * S + 5.032 for 0.723 < S < 0.967  0.839 *S + 0.198 for 0.967 < S < 1.692  2.713 * S − 2.973 for 1.692 < S < 1.939Post Height < −53.233 * S + 105.506 for 1.879 < S < 1.939  −1.406 * S +8.122 for 1.465 < S < 1.879  3.898 * S + 0.353 for 1.035 < S < 1.465 7.535 * S − 3.412 for 0.723 < S < 1.035

B is selected from the group of sets of inequalities consisting of: SetB1: Post Height >  0.254 * S + 0.462 for 0.319 < S < 3.667  2.665 * S +−8.380 for 3.667 < S < 5.000 Post Height < −18.282 * S + 96.357 for4.500 < S < 5.000  −4.663 * S + 35.071 for 2.738 < S < 4.500  2.585 *S + 15.227 for 1.447 < S < 2.738   16.013 * S − 4.204 for 0.319 < S <1.447

Set B2: Post Height >  0.269 * S + 0.456 for 0.380 < S < 3.016  3.051 *S − 7.936 for 3.016 < S < 4.167 Post Height < −14.766 * S + 66.309 for3.667 < S < 4.167  −3.952 * S + 26.654 for 2.315 < S < 3.667  3.108 *S + 10.310 for 1.278 < S < 2.315   14.542 * S − 4.303 for 0.389 < S <1.278   88.444 * S − 33.051 for 0.380 < S < 0.389

Set B3: Post Height >  0.191 * S + 0.626 for 0.472 < S < 2.181  2.135 *S − 3.613 for 2.181 < S < 3.095 53.475 * S − 162.511 for 3.095 < S <3.175 Post Height < −5.095 * S + 23.450 for 2.222 < S < 3.175  0.805 *S + 10.339 for 1.381 < S < 2.222 10.251 * S − 2.706 for 0.572 < S <1.381 24.420 * S − 10.810 for 0.472 < S < 0.572

C is selected from the group of sets of inequalities consisting of: SetC1: Post Height >  0.322 * S + 0.359 for 0.233 < S < 6.667  2.202 * S −12.179 for 6.667 < S < 8.333 Post Height < −25.555 * S + 219.122 for7.778 < S < 8.333  −5.585 * S + 63.794 for 4.000 < S < 7.778  3.214 *S + 28.600 for 1.793 < S < 4.000   21.749 * S − 4.633 for 0.233 < S <1.793

Set C2: Post Height >  0.277 * S + 0.593 for 0.250 < S < 5.182  2.342 *S − 10.111 for 5.182 < S < 7.222 Post Height < −13.149 * S + 101.763 for6.111 < S < 7.222  −4.885 * S + 51.265 for 3.333 < S < 6.111  4.291 *S + 20.680 for 1.520 < S < 3.333  20.788 * S − 4.395 for 0.251 < S <1.520 161.000 * S − 39.588 for 0.250 < S < 0.251

Set C3: Post Height >  0.277 * S + 0.591 for 0.278 < S < 4.425  1.916 *S − 6.663 for 4.425 < S < 6.111 Post Height < −21.337 * S + 135.438 for5.556 < S < 6.111  −4.985 * S + 44.588 for 3.175 < S < 5.556  2.749 *S + 20.031 for 1.560 < S < 3.175  18.321 * S − 4.260 for 0.278 < S <1.560

and D is selected from the group of sets of inequalities consisting of:Set D1: Post Height >  0.257 * S + 0.327 for 0.208 < S < 7.778  1.977 *S − 13.044 for 7.778 < S < 9.444 Post Height < −36.195 * S + 347.445 for8.889 < S < 9.444  −5.777 * S + 77.062 for 4.833 < S < 8.889  1.950 *S + 39.718 for 2.222 < S < 4.833  20.301 * S + −1.058 for 0.389 < S <2.222  34.481 * S + −6.574 for 0.208 < S < 0.389

Set D2: Post Height >  0.322 * S + 0.359 for 0.233 < S < 6.667  2.202 *S + −12.179 for 6.667 < S < 8.333 Post Height < −25.555 * S + 219.122for 7.778 < S < 8.333  −5.585 * S + 63.794 for 4.000 < S < 7.778 3.214 * S + 28.600 for 1.793 < S < 4.000  21.749 * S + −4.633 for 0.233< S < 1.793

Set D3: Post Height >  0.212 * S + 0.600 for 0.264 < S < 4.833  3.017 *S + −12.960 for 4.833 < S < 6.667 Post Height < −12.356 * S + 89.531 for5.556 < S < 6.667  −4.551 * S + 46.170 for 3.175 < S < 5.556  3.850 *S + 19.496 for 1.502 < S < 3.175  19.751 * S + −4.387 for 0.264 < S <1.502